Topic Name Description
Course Introduction Course Syllabus
1.1: Order of Operations Tyler Wallace's "Beginning and Intermediate Algebra: Section 0.3, Order of Operations"

Please read section 0.3 to learn about order of operations. The assignment listed under this subunit corresponds to this reading. Mathematics would be useless if some people thought 3 + 4 x 2 = 14 and others thought 3 + 4 x 2 = 11. Understanding the order of operations is the most basic (and important) task of the student of mathematics.

1.1.1: Removing Parentheses Tyler Wallace's "Beginning Algebra Lab Notebook: Order of Operations - Introduction"

Please complete pages 4 to 5 of Wallace's workbook to learn about order of operations. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Remember that the primary rule for order of operations is that things in parentheses be simplified first.

Tyler Wallace's "Order of Operations - Introduction"

Watch the first  video, which introduces you to the order of operations. Please pay attention to the order in which operations are used and the mnemonic PEMDAS and what it stands for. Note that the video does not make use of the equal sign. Please take a look at Saylor Academy's "Revision to MA001 Video" for a detailed explanation of how to solve the two problems presented in the video.

Then, watch the second video. In this video, you will apply PEMDAS to solving problems by first removing parentheses, simplifying exponents, multiplying, dividing, adding, and subtracting. Please understand that regarding multiplication and division, we perform whichever comes first, from left to right.

1.1.2: Absolute Values Tyler Wallace's "Beginning Algebra Lab Notebook: Order of Operations - Absolute Value"

Complete page 7 of Wallace's workbook to apply your knowledge about order of operations with absolute values. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Absolute values tell us how far apart two numbers are, and we need to practice working with absolute value equations.

Tyler Wallace's "Order of Operations - Absolute Value"

Watch this video, paying attention to the examples being used to explain the concept of absolute values. You may refer to the video when doing your homework, if necessary.

1.1.3: Order of Operations on Fractions Tyler Wallace's "Order of Operations - Fractions"

Watch this brief video. Pay attention to the examples being used to explain the concept of four operations on integers. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.

Tyler Wallace's "Beginning Algebra Lab Notebook: Order of Operations - Fractions"

Complete page 6 of Wallace's workbook to practice with the four operations on integers. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Fractions allow us to manipulate complicated expressions that include division. Being able to work with fractions allows us to simplify (and often avoid) division.

1.1.4: Homework Assessment Tyler Wallace's "Beginning and Intermediate Algebra: "Practice - Order of Operation"

Review the topics covered in the course so far, and then complete these exercises. Answer only the odd-numbered questions in numbers 1 to 25.

1.2: Simplify Algebraic Expressions Tyler Wallace's "Beginning and Intermediate Algebra: Section 0.4: Properties of Algebra"

Read this section to learn how to evaluate algebraic expressions for some given values.

1.2.1: Evaluate Expressions Tyler Wallace's "Beginning Algebra Lab Notebook: Simplify Algebraic Expressions - Evaluate"

Complete page 8 of Wallace's workbook to evaluate algebraic expressions. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Tyler Wallace's "Simplify Algebraic Expressions - Evaluate"

Watch this brief video, which discusses how to evaluate expressions. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.

1.2.2: Combine Like Terms Tyler Wallace's "Beginning Algebra Lab Notebook: Simplify Algebraic Expressions - Combine Like Terms"

Complete page 9 of Wallace's workbook for practice with combining like terms. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Tyler Wallace's "Simplify Algebraic Expressions - Combine Like Terms"

Watch this brief video, paying attention to the examples do the practice problem set on to access your understanding. You may watch the video as often as you please. You may refer to the video when doing your homework if necessary.

1.2.3: Distributive Properties Tyler Wallace's "Beginning Algebra Lab Notebook: Simplify Algebraic Expressions - Distributive Properties"

Complete page 10 of Wallace's workbook for practice with simplifying algebraic expressions, using the distributive property. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Tyler Wallace's "Simplify Algebraic Expressions - Distributive Property"

Watch this brief video. Note that when we distribute, we take into consideration the sign of the number we are distributing. Particularly, if you distribute a negative number over a positive number you get a negative number and vice versa. Be careful when you distribute negative numbers.

1.2.4: Distribute and Combine Like Terms Tyler Wallace's "Beginning Algebra Lab Notebook: Simplify Algebraic Expressions - Distribute and Combine"

Complete page 11 of Wallace's workbook for practice with distributing and combining like terms. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Tyler Wallace's "Simplify Algebraic Expressions - Distribute and Combine"

Watch this brief video. As we have already familiarized ourselves with distribution in subunit 1.2.3 above, this lesson will expand on that to combine like terms. The goal here is to be able to distribute and combine terms that are alike: terms with the same variable or group of variables and exponents. Remember that combining like terms is simply adding or subtracting the numerical coefficients in the like terms.

1.2.5: Homework Assessment Tyler Wallace's "Beginning and Intermediate Algebra: Practice - Properties of Algebra"

Review the topics covered above, watch the videos, and then do the exercises provided in the link above. Answer every other odd question in 1-81.

1.3.1: Equality Property of Addition and Multiplication Tyler Wallace's "Linear Equations - One Step Equations"

Watch this brief video. Note that the take-home message here is that in linear equations, and in other equations you will handle in the future, we can add and multiply same expressions on both sides of the equation. We must do the same thing to each side in order to keep the balance, otherwise we change the solutions to our problem.

1.3.2: Solving One Step Equations Tyler Wallace's "Beginning and Intermediate Algebra: Section 1.1: Solving Linear Equations - One Step Equations"

Read this section, beginning on page 28, to learn how to solve "one step equations."

Tyler Wallace's "Beginning Algebra Lab Notebook: Linear Equations - One Step Equations"

Complete page 12 of Wallace's workbook for practice with solving one step linear equations.

Khan Academy: "Example: Two-Step Equation with x/4 Term"

Watch this brief optional video if you feel like you need additional help with this topic.

1.3.3: Solving Two Step Equations Tyler Wallace's "Beginning and Intermediate Algebra: Section 1.2: Linear Equations - Two Step Equations"

Read section 1.2 on page 33 to learn how to solve "two step equations." Note that the assignment at the end of this subunit corresponds with this reading.

Tyler Wallace's "Beginning Algebra Lab Notebook: Linear Equations - Two Step Equations"

Complete page 13 of Wallace's workbook for practice with solving two step linear equations. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Tyler Wallace's "Linear Equations - Two Step Equations"

Watch this video to learn how to solve two-step equations. You may watch the video as often as you please. You may refer to the video when doing your homework if necessary.

1.3.4: Solving General Linear Equations in One Variable Tyler Wallace's "Beginning and Intermediate Algebra: Section 1.3: Solving Linear Equations - General Linear Equations"

Read this section, beginning on page 37, to learn how to solve general linear equations.

Khan Academy: "Solving Ax + B = C"

Watch this brief optional video if you feel like you need additional help with this topic.

Tyler Wallace's "Beginning Algebra Lab Notebook: Linear Equations - General"

Complete page 14 of Wallace's workbook for practice with simplifying general linear equations with one variable. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions. Note that the video contains a small error in its discussion of Practice B, which will affect the final answer.

Tyler Wallace's "Linear Equations - General"

Watch this brief video, paying attention to the examples being used to explain how to solve general linear equations with one variable. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary. Please note that there is a small math error at the 3:15-minute mark in the video; the 5 is not distributed correctly on the right side. The correct answer to the example is -6. For a full explanation of how to solve the problem, please read the "Revision to Tyler Wallace's 'Linear Equations in One Variable'".

1.3.5: Solving Equations involving Fractions Tyler Wallace's "Beginning and Intermediate Algebra: Section 1.4: Solving Linear Equations - Fractions"

Read this section, beginning on page 43, to learn how to solve equations involving fractions.

Tyler Wallace's "Beginning Algebra Lab Notebook: Linear Equations - Fractions and Linear Equations - Distributing with Fractions"

Complete pages 15 and 16 of Wallace's workbook for practice with solving equations with fractions. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Tyler Wallace's "Linear Equations - Fractions" and "Linear Equations in One Variable - Distributing with Fractions"

The first video demonstrates how to solve equations that involve fractions. The second explains how to distribute fractions in linear equations that have one variable. You may watch the videos as often as you please. You may refer to the videos when doing your homework, if necessary.

Khan Academy: "Solving Ax + B = C", "Identifying Fraction Parts", and "Equivalent Fractions Example"

Watch these brief optional videos if you feel like you need additional help with this topic.

1.3.6: Homework Assessment Tyler Wallace's "Beginning and Intermediate Algebra: Practice - Two Step Problems"

Answer every other odd-numbered problem in questions 1 through 39.

Tyler Wallace's "Beginning and Intermediate Algebra: Practice - General Linear Equations"

Answer every other odd-numbered problem in questions 1 through 49.

Tyler Wallace's "Beginning and Intermediate Algebra: Practice - Fractions"

Answer every other odd-numbered problem in questions 1 through 29.

1.4: Formulas Tyler Wallace's "Beginning and Intermediate Algebra: Section 1.5: Solving Linear Equations - Formula"

Read this section. You now have the skills to take a formula that relates two or more quantities and solve it for whichever quantity you want. Notice how this allows us to use formulas in many ways. This is also great practice for algebra skills we will use throughout the course.

1.4.1: Two Step Formulas Tyler Wallace's "Beginning Algebra Lab Notebook: Formulas - Two Step Formulas"

Complete page 17 of Wallace's workbook for practice with two-step formulas. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Tyler Wallace's "Formulas - Two Step Formulas"

Watch this brief video, paying attention to the examples being used to explain two-step formulas. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.

1.4.2: Multi-Step Formulas Tyler Wallace's "Beginning Algebra Lab Notebook: Formulas - Multi-Step Formulas"

Complete page 18 of Wallace's workbook for practice with multi-step formulas. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Tyler Wallace's "Formulas - Multi-Step Formulas"

Watch this brief video, which explains how to use multistep formulas. Also, note that the four properties you studied earlier in this course are also applicable here. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.

1.4.3: Fractions Tyler Wallace's "Beginning Algebra Lab Notebook: Formulas - Fractions"

Complete page 19 of Wallace's workbook for practice with clearing fractions. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Tyler Wallace's "Formulas - Fractions"

Watch this five-minute video, paying attention to the examples being used to explain how to clear fractions when using formulas. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.

1.4.4: Homework Assessment Tyler Wallace's "Beginning and Intermediate Algebra: Practice - Formulas"

Review the topics, watch the videos, and do the exercises provided in the link above. Answer the odd-numbered questions from 1 to 49. Solutions are given on page 2 of the PDF.

1.5: Absolute Value Equations Tyler Wallace's "Beginning and Intermediate Algebra: Section 1.6: Solving Linear Equations - Absolute Value"

Read this section. The equations x - 3 = 2 and |x - 3| = 2 are very different from each other, but they are also closely. Notice how we turn an equation with absolute values into two equations without absolute values. Note that this reading covers all the material you need to know for subunits 1.5.1-1.5.3.

1.5.1: Two Solutions Tyler Wallace's "Beginning Algebra Lab Notebook: Absolute Value - Two Solutions"

Complete page 20 of Wallace's workbook to practice solving absolute value equations with two solutions. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Tyler Wallace's "Absolute Value - Two Solutions"

Watch this five-minute video, which explains how two solutions are applied to absolute value equations. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.

1.5.2: Isolate Absolute Value Tyler Wallace's "Beginning Algebra Lab Notebook: Absolute Value - Isolate Absolute"

Complete page 21 of Wallace's workbook for practice with isolating absolute values. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions. (Note that the final term in Example B in the workbook should be -31 rather than -32).

Tyler Wallace's "Absolute Value - Isolate Absolute"

Watch this five-minute video, paying attention to the examples being used to explain how to isolate an absolute value. Watch the video as many times as necessary to understand the concept. You may refer to the video when doing your homework, if necessary.

1.5.3: Two Absolute Values Tyler Wallace's "Absolute Value Equations - Two Absolutes"

Watch this five-minute video, which demonstrates how to solve absolute value equations when two absolute values are involved. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.

Tyler Wallace's "Beginning Algebra Lab Notebook: Absolute Value - Two Absolutes"

Complete page 22 of Wallace's workbook to practice solving for variables with equations that contain two absolute values.

1.5.4: Homework Assessment Tyler Wallace's "Beginning and Intermediate Algebra: Practice - Absolute Value Equations"

Review the topics covered in the course so far, and then complete the exercises linked above. Work on only the odd-numbered questions for numbers 1 through 35. Solutions are given on page 2 of the PDF.

1.6: Introduction to Problem Solving (Word Problems) Tyler Wallace's "Beginning and Intermediate Algebra: Section 1.8: Linear Equations - Number and Geometry"

Read this section. Word problems are about gathering information, turning it into equations, and then using the equations to solve the stated problem. Please focus on the various ways that we turn English statements into mathematical equations.

1.6.1: Number Problems Tyler Wallace's "Word Problems - Number Problems"

Watch this five-minute video, paying attention to the examples being used to learn how to translate words into mathematical expressions. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.

Tyler Wallace's "Beginning Algebra Lab Notebook: Word Problems - Number Problems"

Complete page 23 of Wallace's workbook to apply your knowledge of consecutive even and odd integers. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

1.6.2: Consecutive Integers Tyler Wallace's "Word Problems - Consecutive Integers"

Watch this five-minute video, paying attention to the examples being used to learn how to solve problems with consecutive integers. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.

Tyler Wallace's "Beginning Algebra Lab Notebook: Word Problems - Consecutive Integers"

Complete page 24 of Wallace's workbook to practice solving word problems with consecutive integers. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

1.6.3: Consecutive Even/Odd Integers Tyler Wallace's "Beginning Algebra Lab Notebook: Word Problems - Consecutive Even/Odd"

Complete page 25 of Wallace's workbook to apply your knowledge of consecutive even and odd integers. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Tyler Wallace's "Word Problems - Consecutive Even/Odd"

Watch this five-minute video, which shows how to solve problems with consecutive even and odd integers. You may watch the video as often as you please. You may refer to the video when doing

1.6.4: Angles of Triangles Tyler Wallace's "Beginning Algebra Lab Notebook: Word Problems - Triangles"

Complete page 26 of Wallace's workbook to practice solving word problems that involve angles of triangles. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Tyler Wallace's "Word Problems - Triangles"

Watch this five-minute video, which explains how to solve problems using angles of triangles. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.

1.6.5: Perimeter of Rectangles Tyler Wallace's "Beginning Algebra Lab Notebook: Word Problems - Perimeter"

Complete page 27 of Wallace's workbook to practice solving word problems involving perimeters. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Tyler Wallace's "Word Problems - Perimeter"

Watch this five-minute video, paying attention to the examples that explain how to problem solve with the perimeter of rectangles. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.

1.6.6: Homework Assessment Tyler Wallace's "Beginning and Intermediate Algebra: Practice - Number and Geometry Problems"

Review the topics covered so far in this course, and attempt the odd numbered exercises in questions 1 to 45. Solutions are on page 4 of the PDF.

1.7.1: Variable Age Now Tyler Wallace's "Beginning and Intermediate Algebra: Section 1.9: Solving Linear Equations - Age Problems"

Tyler Wallace's "Beginning Algebra Lab Notebook: Age Problem - Variable Now"

Complete page 28 of Wallace's workbook to practice solving word problems that ask you to solve for a person's age. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Tyler Wallace's "Age Problems - Variable Now"

Watch this five-minute video, which demonstrates how to solve age problems. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.

Khan Academy: "Age Word Problems 1 and 2"

Watch these brief optional videos if you feel like you need additional help with this topic.

1.7.2: Given Sum Ages Now Tyler Wallace's "Age Problems - Sum Now"

Watch this five-minute video, paying attention to the examples being used to further explain how to solve age problems. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.

Tyler Wallace's "Beginning Algebra Lab Notebook: Age Problem - Sum Now and Variable Time"

Complete pages 29 and 30 of Wallace's workbook to practice solving word problems to determine ages of a person in the past based on information given about the person's age now.

Khan Academy: "Age Word Problem 3"

Watch this brief optional video if you feel like you need additional help with this topic.

1.7.3: Homework Assessment Tyler Wallace's "Beginning and Intermediate Algebra: Practice - Age Problems"

Answer the odd numbered problems for questions 1 to 39. Solutions are on page 4 of the PDF.

Unit 1 Practice Test Tyler Wallace's "Beginning and Intermediate Algebra: Unit 1 Practice Test"

Review Unit 1 before taking this practice test. Be sure that you are ready before taking the practice test, as it will give you a clear picture of what you know and the areas you need to review, if necessary. This is very important. You may review the problems in the work pages in addition to watching the videos to prep for the practice test. When you have finished this practice test, check your answers against Saylor Academy's "Unit 1 Practice Test - Answer Key".

2.1: Inequalities Tyler Wallace's "Beginning and Intermediate Algebra: Section 3.1: Inequalities - Solve and Graph Inequalities"

Read this section. Note the difference in meaning among "equal," "less than," and "less than or equal," and the symbols we use for these ideas. Focus on how the steps for solving inequalities are different than for solving equations.

2.1.1: Graphing Inequalities Tyler Wallace's "Inequalities - Graphing"

Watch this four-minute video, paying attention to the examples being used to explain graphing inequalities. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary. In this unit, the operations on the terms are very similar to solving equations. Here, we make use of inequality instead of an equal sign. The inequality sign switches/flips when you multiply or divide both sides by a negative number.

Tyler Wallace's "Beginning Algebra Lab Notebook: Inequalities - Graphing"

Complete page 32 of Wallace's workbook to practice graphing inequalities on a number line. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Khan Academy: "Graphing Inequalities", "Graphing Linear Inequalities in Two Variables Example 2", and "Graphing Linear Inequalities in Two Variables Example 3"

Watch these brief optional videos if you feel like you need additional help with this topic.

2.1.2: Interval Notation Tyler Wallace's "Beginning Algebra Lab Notebook: Inequalities - Interval Notation"

Complete page 33 of Wallace's workbook to practice with interval notation. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

We use plots, graphs, and pictures to help us understand and communicate. Interval notation is a very visual way to communicate inequalities, and it also gives us visual techniques for solving them.

Tyler Wallace's "Inequalities - Interval Notation"

Watch this three-minute video, paying attention to the examples being used to explain interval notation. Note when to use a square bracket and a round bracket. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.

Watch this brief optional video if you feel like you need additional help with this topic.

2.1.3.1: Solving Linear Inequalities Tyler Wallace's "Beginning Algebra Lab Notebook: Inequalities - Solving"

Complete page 34 of Wallace's workbook to practice solving inequalities. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Tyler Wallace's "Inequalities - Solving"

Watch this five-minute video, paying attention to the examples which provide a linear approach to solving inequalities. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.

2.1.3.2: Solve Compound Inequalities (Tripartite) Tyler Wallace's "Inequalities - Tripartite"

Watch this five-minute video. Note that compound or tripartite inequalities are very similar to linear inequalities, except for the way they are structured. Bear in mind that in the tripartite inequalities, we will be balancing the left center and right. This means whatever you decide to do to the center in order to get the variable in question by itself, you have to do the same to the other two parts of the inequality. Notice also that if you divide or multiply through by a negative number, then you have to flip the inequality signs.

Tyler Wallace's "Beginning Algebra Lab Notebook: Inequalities - Tripartite"

Complete page 35 of Wallace's workbook to practice solving inequalities. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

2.1.4: Homework Assessment Tyler Wallace's "Beginning and Intermediate Algebra: Practice - Solve and Graph Inequalities"

Answer odd-numbered problems 1 to 37.

Tyler Wallace's "Beginning and Intermediate Algebra: Practice - Compound Inequalities"

Answer all problems, from 1 to 19.

2.2.1: Point and Lines Tyler Wallace's "Beginning and Intermediate Algebra: Section 2.1: Graphing - Point and Lines"

Read this section, on pages 89 to 93. One of our most powerful tools is visualization; graphs and XY coordinates comprise the foundation of "seeing" math. Getting comfortable when working with points and lines in a coordinate system is the main point of this section.

Read the following short article for a brief description of the four quadrants of a Cartesian graph.

Tyler Wallace's "Beginning Algebra Lab Notebook: Graphing and Slope - Points and Lines"

Complete page 36 of Wallace's workbook for practice with graphing based on points provided or equation of the line provided. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Tyler Wallace's "Graphing and Slope - Points and Lines"

Watch this five-minute video, which discusses points and lines in graphing and slopes. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.

Watch these brief optional videos if you feel like you need additional help with this topic.

2.2.2: Slope from a Graph Tyler Wallace's "Beginning and Intermediate Algebra: Section 2.2: Graphing - Slope"

Read this section, which focuses on one fundamental property of the line: its slope. The slope tells us how much the line rises as we move to the right. There are several ways to talk about this one idea.

Tyler Wallace's "Beginning Algebra Lab Notebook: Graphing and Slope - Slope from a Graph"

Complete page 37 of Wallace's workbook to work on determining the slope of a line, given the line on a graph. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Tyler Wallace's "Graphing and Slope - Slope from Graph"

Watch this four-minute video, paying attention to the examples being used to explain the slope of a graph. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.

2.2.3: Slope from Two Points Tyler Wallace's "Beginning Algebra Lab Notebook: Graphing and Slope - Slope from Two Points"

Complete page 38 of Wallace's workbook to work on finding the slope when given two sets of points. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Tyler Wallace's "Graphing and Slope - Slope from Two Points"

Watch this five-minute video. Take note of the examples used in the video to explain how to find the slope using two points on the graph. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.

Khan Academy: "Point-Slope and Standard Form"

Watch this brief optional video if you feel like you need additional help with this topic.

2.2.4: Homework Assessment Tyler Wallace's "Beginning and Intermediate Algebra: Practice - Points and Lines"

Work through problems 1, 2, and every other odd problem from question 3 through 21.

Tyler Wallace's "Beginning and Intermediate Algebra: Practice - Slope"

Attempt the odd problems from questions 1 through 29.

2.3: Equations of Lines Tyler Wallace's "Beginning and Intermediate Algebra: Section 2.3: Graphing - Slope-Intercept Form"

Read this section. We know what a line is when we see it plotted. There is more than one useful way to write the equation for a line.

2.3.1: Slope-Intercept Equations Tyler Wallace's "Beginning Algebra Lab Notebook: Equations - Slope Intercept Equation"

Complete page 39 of Wallace's workbook to practice providing the slope intercept equation when given information of the slope and y-intercept, or a graph. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Tyler Wallace's "Equations - Slope Intercept Equation"

Watch this five-minute video to learn about the slope-intercept equation and its applications. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.

Khan Academy: "Multiple Examples of Constructing Linear Equations in Slope-Intercept Form"

Watch this brief optional video if you feel like you need additional help with this topic.

2.3.2: Putting Equations in Intercept Form Tyler Wallace's "Beginning Algebra Lab Notebook: Equations - Put in Intercept Form"

Complete page 40 of Wallace's workbook to practice putting an equation in intercept form. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Tyler Wallace's "Equations - Put in Intercept Form"

Watch this four-minute video to learn about putting equations in intercept form. Understand that sometimes there will be no intercept or slope, in which case the slope or intercept will be zero.

2.3.3: Equation from Graph Tyler Wallace's "Beginning Algebra Lab Notebook: Equations - Graph"

Complete page 41 of Wallace's workbook to work on graphing equations. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Tyler Wallace's "Equations - Graph"

Watch this five-minute video, paying attention to the examples being used to instruct you on how to graph equations. Be sure that you understand the different parts of the straight line equation and the names that go with them. You may practice by graphing your own lines and seeing if you can label them completely.

2.3.4: Vertical and Horizontal Lines Tyler Wallace's "Beginning Algebra Lab Notebook: Equations - Vertical/Horizontal"

Complete page 42 of Wallace's workbook to practice graphing or finding the equations for vertical and horizontal lines. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Tyler Wallace's "Equations - Vertical/Horizontal"

Watch this two-minute video, which discusses the different characteristics of vertical and horizontal lines. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.

2.3.5: Point-Slope Equations Tyler Wallace's "Beginning Algebra Lab Notebook: Equations - Point Slope"

Complete page 43 of Wallace's workbook to practice finding the point slope equation, given a point the line passes through and the slope. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Tyler Wallace's "Equations - Point Slope"

Watch this five-minute video, paying attention to the examples being used to demonstrate the point-slope equation.

Khan Academy: "Point-Slope and Standard Form"

Watch this brief optional video if you feel like you need additional help with this topic.

2.3.6: Using Two Points to Find the Equation of a Line Tyler Wallace's "Beginning Algebra Lab Notebook: Equations - Given Two Points"

Complete page 44 of Wallace's workbook to practice with finding an equation when given two points. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Tyler Wallace's "Equations - Given Two Points"

Watch this five-minute video, focusing on the examples used to find the equation of the line with two points given.

2.3.7: Homework Assessment Tyler Wallace's "Beginning and Intermediate Algebra: Practice - Slope-Intercept"

Answer every other odd-numbered problem in questions 1 through 41.

Tyler Wallace's "Beginning and Intermediate Algebra: Practice - Point-Slope Form"

Answer every other odd-numbered problem in questions 1 through 51.

2.4: Parallel and Perpendicular Tyler Wallace's "Beginning and Intermediate Algebra: Section 2.5: Graphing - Parallel and Perpendicular Lines"

Read this section. Parallel lines never intersect, which is good to know if you are looking for an intersection! The shortest distance from a line to something else is perpendicular to the line. The slopes for parallel and perpendicular lines have simple relationships to each other (which you should memorize!).

Khan Academy: "Equations of Parallel and Perpendicular Lines"

Watch this brief optional video if you feel like you need additional help with this topic.

2.4.1: Slope Tyler Wallace's "Beginning Algebra Lab Notebook: Parallel and Perpendicular - Slope"

Complete page 45 of Wallace's workbook to practice determining whether lines will be parallel, perpendicular, or neither. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Tyler Wallace's "Parallel and Perpendicular - Slope"

Watch this five-minute video, focusing on the examples used to explain how to find the slope of parallel and perpendicular lines. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.

2.4.2: Equations Tyler Wallace's "Beginning Algebra Lab Notebook: Parallel and Perpendicular - Equations"

Complete page 46 of Wallace's workbook to find the equations of parallel and perpendicular lines. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Tyler Wallace's "Parallel and Perpendicular - Equations"

Watch this five-minute video to learn about equations used for parallel and perpendicular lines.

2.4.3: Homework Assessment Tyler Wallace's "Beginning and Intermediate Algebra: Practice - Parallel and Perpendicular Lines"

Answer the odd-numbered problems for questions 1 through 47.

2.5: Distance and Rate Problems Tyler Wallace's "Beginning and Intermediate Algebra: Section 1.10: Solving Linear Equations - Distance, Rate and Time"

Read this section. The relationship among distance, rate, and time is one of the simplest and most fundamental of physics and engineering. Notice how d = rt is a relationship that can be solved for any of the three variables.

2.5.1: Opposite Directions Tyler Wallace's "Beginning Algebra Lab Notebook: Distance - Opposite Directions"

Complete page 47 of Wallace's workbook to practice solving distance problems. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Tyler Wallace's "Distance - Opposite Directions"

Watch this five-minute video, which demonstrates how to solve distance problems involving opposite directions. In working with distance and rate problems, it will be helpful if you begin every question by first drawing a picture and translating the picture into a table as demonstrated in the video. Finally, apply the formula to get the required answer. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.

2.5.2: Catch-Up Tyler Wallace's "Beginning Algebra Lab Notebook: Distance - Catch Up"

Complete page 48 of Wallace's workbook to practice solving distance problems. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Two objects may be moving in the same direction or in different directions. This is the simplest relationship between two moving objects. "Catch-Up" problems are about moving in the same direction but at different speeds.

Tyler Wallace's "Distance - Catch Up"

Watch this five-minute video, which demonstrates distance problems in which one person is trying to catch up with another person. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.

2.5.3: Total Time Tyler Wallace's "Beginning Algebra Lab Notebook: Distance - Total Time"

Complete page 49 of Wallace's workbook to practice solving distance problems. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Tyler Wallace's "Distance - Total Time"

Watch this five-minute video, paying attention to the distance and rate problems shown to demonstrate the concept of total time. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.

2.5.4: Homework Assessment Tyler Wallace's "Beginning and Intermediate Algebra: Practice - Distance, Rate, and Time Problems"

Answer the odd-numbered problems for questions 1 through 37.

Unit 2 Practice Test Tyler Wallace's "Beginning and Intermediate Algebra: Unit 2 Practice Test"

Review Unit 2 before taking this practice test. Be sure that you are ready before taking the practice test, as it will give you a clear picture of what you know and the areas you need to review, if necessary. You may review the problems in the work pages in addition to watching the videos to prep for the practice test. When you have finished this practice test, you may check your answers against the "Unit 2 Practice Test - Answer Key".

3.1.1: Rules of Exponents Tyler Wallace's "Beginning and Intermediate Algebra: Section 5.1: Polynomials - Exponent Properties"

Read this section. Polynomials are all about adding and multiplying powers of x. Notice that we have specific rules that govern multiplying and dividing powers of x and raising a power of x to another power.

3.1.1.1: Product Rule Tyler Wallace's "Beginning Algebra Lab Notebook: Exponents - Product Rule"

Complete page 51 of Wallace's workbook to practice implementing the product rule. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Tyler Wallace's "Exponents - Product Rule"

Watch this three-minute video, which discusses the product rule for exponents.

3.1.1.2: Quotient Rule Tyler Wallace's "Beginning Algebra Lab Notebook: Exponents - Quotient Rule"

Complete page 52 of Wallace's workbook to practice implementing the quotient rule. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Tyler Wallace's "Exponents - Quotient Rule" and MathIsPower4U's "Simplify Exponential Expressions - Quotient Rule"

Watch these two videos, which discuss the quotient rule for exponents.

3.1.1.3: Power Rule Tyler Wallace's "Beginning Algebra Lab Notebook: Exponents - Power Rules"

Complete page 53 of Wallace's workbook to practice implementing the power rule. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Tyler Wallace's "Exponents - Power Rules"

Watch these two videos, which discuss the power rule for exponents.

3.1.1.4: Zero Exponents Tyler Wallace's "Beginning and Intermediate Algebra: Section 5.2 Polynomials - Negative Exponents"

Read this section. Notice that a negative exponent in the denominator is the same as a positive exponent in the numerator. Conversely, a negative exponent in the numerator is the same as a positive exponent in the denominator.

Tyler Wallace's "Beginning Algebra Lab Notebook: Exponents - Zero"

Complete page 54 of Wallace's workbook to practice with the zero power rule. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Tyler Wallace's "Exponents - Zero"

Watch this four-minute video, which discusses the zero power rule with exponents. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.

3.1.1.5: Negative Exponents Tyler Wallace's "Beginning Algebra Lab Notebook: Exponents - Negative Exponents"

Complete page 55 of Wallace's workbook to practice with negative exponents. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Tyler Wallace's "Exponents - Negative Exponents" and MathIsPower4U's "Simplify Exponential Expressions with Negative Exponents"

Watch these two videos, which discuss rules for negative exponents.

Khan Academy: "Raising a Number to the 0th and 1st Power"

Watch this video, which shows a short proof of the zero exponent.

3.1.2: Properties Tyler Wallace's "Beginning Algebra Lab Notebook: Exponents - Properties"

Complete page 56 of Wallace's workbook to solve equations using the properties of exponents. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Tyler Wallace's "Exponents - Properties" and MathIsPower4U's "Simplify an Exponential Expression Video Series"

Watch each of these videos, focusing on the examples used that demonstrate how to simplify exponents with the properties and rules you have learned so far, i.e., product rule, quotient rule, etc.

3.1.3: Homework Assessment Tyler Wallace's "Beginning and Intermediate Algebra: Practice - Exponent Properties"

Answer the odd-numbered problems for questions 1 through 43.

Tyler Wallace's "Beginning and Intermediate Algebra: Practice - Negative Exponents"

Answer the odd-numbered problems for questions 1 through 39.

3.2: Scientific and Decimal Notation Tyler Wallace's "Beginning and Intermediate Algebra: Section 5.3: Polynomials - Scientific Notation"

Read this section. Scientific notation allows us a general idea of the size of a number with a glance at the exponent, instead of counting places before or after a decimal point.

3.2.1: Convert Tyler Wallace's "Beginning Algebra Lab Notebook: Scientific Notation - Convert"

Complete page 57 of Wallace's workbook to practice with converting between standard and scientific notation. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Tyler Wallace's "Scientific Notation - Convert"

Watch this five-minute video, which demonstrates how to convert between standard and scientific notation.

3.2.2: Close to Scientific Tyler Wallace's "Beginning Algebra Lab Notebook: Scientific Notation - Close to Scientific"

Complete page 58 of Wallace's workbook for more practice with scientific notation. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Tyler Wallace's "Scientific a Notation - Close to Scientific"

Watch this four-minute video, paying attention to the examples being used to further explain scientific notation. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.

3.2.3: Multiply/Divide Tyler Wallace's "Beginning Algebra Lab Notebook: Scientific Notation - Multiply/Divide"

Complete page 59 of Wallace's workbook for more practice with scientific notation. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Tyler Wallace's "Scientific Notation - Multiply/Divide"

Watch this three-minute video, which discusses how to multiply and divide with scientific notation.

3.2.4: Multiply/Divide Leaving Answer in Decimal Notation Tyler Wallace's "Beginning Algebra Lab Notebook: Scientific Notation - Multiply/Divide Where Answer is Not in Scientific Notation"

Complete page 60 of Wallace's workbook to practice with multiplying and dividing scientific notation with a result that is not in scientific notation. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Tyler Wallace's "Scientific Notation - Multiply/Divide Where Answer Is Not in Scientific Notation"

Click on the link above and watch this four-minute video, which addresses multiplication and division and then converting the answer to scientific notation.

3.2.5: Homework Assessment Tyler Wallace's "Beginning and Intermediate Algebra: Practice - Scientific Notation"

Answer the odd-numbered problems for questions 1 through 41.

3.3.1: Evaluate Tyler Wallace's "Beginning and Intermediate Algebra: Section 5.4: Polynomials - Introduction to Polynomials"

Read this section. Evaluating a polynomial is simply plugging in a value for the variable and then simplifying.

Tyler Wallace's "Polynomials - Evaluate"

Watch this five-minute video, which provides definitions and characteristics of polynomials and gives examples of evaluating polynomials.

Complete page 62 of Wallace's workbook to practice adding and subtracting polynomials. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Tyler Wallace's "Polynomials - Add and Subtract"

Watch this four-minute video, paying attention to the examples being used to add and subtract polynomials.

3.3.3.1: Monomial by Polynomial Tyler Wallace's "Beginning and Intermediate Algebra: Section 5.5: Polynomials - Multiplying Polynomials"

Read this section. Multiplying polynomials is all about being careful with distribution (focus on how parentheses are used to make sure we distribute correctly) and following the rules for exponents (focus on how we use xp xq = xp+q).

Tyler Wallace's "Beginning Algebra Lab Notebook: Polynomials - Multiply by Monomials"

Complete page 63 of Wallace's workbook to practice multiplying by monomials. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Tyler Wallace's "Polynomials - Multiply by Monomial"

Watch this three-minute video, paying attention to the examples being used to explain how to multiply by monomials.

3.3.3.2: Binomial by Binomial (FOIL) Tyler Wallace's "Beginning Algebra Lab Notebook: Polynomials - Multiply by Binomials"

Complete page 64 of Wallace's workbook to practice multiplying by binomials. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Tyler Wallace's "Polynomials - Multiply by Binomials"

Watch this four-minute video, paying attention to the explain of how to multiply binomials.

3.3.3.3: Multiply with Trinomials Tyler Wallace's "Beginning Algebra Lab Notebook: Polynomials - Multiply by Trinomials"

Complete page 65 of Wallace's workbook to practice multiplying by trinomials. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Tyler Wallace's "Polynomials - Multiply by Trinomials"

Watch this five-minute video, paying attention to the explanation of how to multiply trinomials.

3.3.3.4: Multiply Monomial by Two Binomials Tyler Wallace's "Beginning Algebra Lab Notebook: Polynomials - Multiply Monomials and Binomials"

Complete page 66 of Wallace's workbook to practice multiplying monomials by binomials. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Tyler Wallace's "Polynomials - Multiply Monomial by Binomials"

Watch this four-minute video, paying attention to the examples being used to explain how to multiply monomials by two binomials.

3.3.4.1: Sums and Difference Tyler Wallace's "Beginning and Intermediate Algebra: Section 5.6: Polynomials - Multiply Special Products"

Read this section. The idea of this section is to point out a few nice and important special cases of polynomial multiplication. Memorize these special products and it will pay off big later!

Tyler Wallace's "Beginning Algebra Lab Notebook: Polynomials - Sums and Difference"

Complete page 67 of Wallace's workbook to practice multiplying monomials by binomials. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Tyler Wallace's "Polynomials - Sum and Difference", MathIsPower4U's "Simplify an Expression Involving Squares of Binomials", and TheLearningPub's "Factoring Polynomials - Difference of two Squares"

Watch these videos, paying attention to the examples used to explain sums and differences with polynomials.

3.3.4.2: Perfect Square Tyler Wallace's "Beginning Algebra Lab Notebook: Polynomials - Perfect Square"

Complete page 68 of Wallace's workbook to practice with perfect squares. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Tyler Wallace's "Polynomials - Perfect Square"

Watch these videos, which discuss the perfect square shortcut.

3.3.5: Homework Assessment Tyler Wallace's "Beginning and Intermediate Algebra: Practice - Introduction to Polynomials"

Answer every other odd numbered problem for questions 1 through 41.

Tyler Wallace's "Beginning and Intermediate Algebra: Practice - Multiply Polynomials"

Answer every other odd numbered problem for questions 1 through 39.

Tyler Wallace's "Beginning and Intermediate Algebra: Practice - Multiply Special Products"

Answer every other odd numbered problem for questions 1 through 39.

3.4.1: Divide a Polynomial by Monomial Tyler Wallace's "Beginning and Intermediate Algebra: Section 5.7: Polynomials - Divide Polynomials"

Read this section. Dividing polynomials is just the same as the long division you learned in elementary school. It is also great practice in solidifying your skills in exponents and multiplication. Pay special attention to how the exponents work as place holders just as the digits in the 1s, 10s, 100s, and so forth, places did for us in elementary school.

Tyler Wallace's "Beginning Algebra Lab Notebook: Division - By Monomials"

Complete page 69 of Wallace's workbook to practice dividing monomials. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Tyler Wallace's "Division By Monomials"

Watch these videos, which discuss division by monomials.

3.4.2: Divide a Polynomial by a Polynomial Tyler Wallace's "Beginning Algebra Lab Notebook: Division By Polynomials"

Complete page 70 of Wallace's workbook to practice dividing polynomials. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Tyler Wallace's "Beginning Algebra Lab Notebook: Division - Missing Terms"

Complete page 71 of Wallace's workbook for more practice with dividing polynomials. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Tyler Wallace's "Division - Polynomials"

Watch these videos, paying attention to the examples used to explain the division of polynomials. You may watch the videos as often as you please. You may refer to the video when doing your homework, if necessary.

3.4.3: Homework Assessment Tyler Wallace's "Beginning and Intermediate Algebra: Practice - Divide Polynomials"

Answer odd-numbered problems for questions 1 through 43. Keep in mind that you are allowed to watch the videos as often as you please to help you answer the homework problems.

Unit 3 Practice Test Tyler Wallace's "Beginning and Intermediate Algebra: Unit 3 Practice Test"

Review Unit 3 before clicking on the link above to take the practice test. Be sure that you are ready before taking the practice test, as it will give you a clear picture of what you know and the areas you need to review, if necessary. You may review the problems in the work pages in addition to watching the videos to prep for the practice test. When you have finished this practice test, you may check your answers against the "Unit 3 Practice Test - Answer Key"

4.1: Greatest Common Factor (GCF) and Grouping Tyler Wallace's "Beginning and Intermediate Algebra: Section 6.1: Factoring - Greatest Common Factor"

Read this section. Pay special attention to page 212.

4.1.1: Find the GCF Tyler Wallace's "Beginning Algebra Lab Notebook: GCF and Grouping - Find the GCF"

Complete page 73 of Wallace's workbook to practice finding the greatest common factor. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Tyler Wallace's "GCF and Grouping - Find GCF"

Watch this two-minute video, which discusses how to find the Greatest Common Factor (GCF). You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.

4.1.2: Factor the GCF Tyler Wallace's "Beginning Algebra Lab Notebook: GCF and Grouping - Factor GCF"

Complete page 74 of Wallace's workbook to practice factoring the greatest common factor. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Tyler Wallace's "GCF and Grouping - Factor GCF" and MathIsPower4U's "Factor and Solve a Polynomial Equation"

Watch these videos to learn how to factor the Greatest Common Factor (GCF).

4.1.3: Grouping Tyler Wallace's "Beginning and Intermediate Algebra: Section 6.2: Factoring - Grouping"

Read this section. Pay special attention to page 216.

Tyler Wallace's "Beginning Algebra Lab Notebook: GCF and Grouping - Binomial GCF"

Complete page 75 of Wallace's workbook to practice factoring the greatest common factor. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Tyler Wallace's "GCF and Grouping - Grouping" and AlgebraHelpForHumans' "Factor by Grouping"

Watch these videos, which discuss the GCF and grouping methods. You may watch the videos as often as you please. You may refer to the videos when doing your homework, if necessary.

4.1.4: Grouping with Order Change Tyler Wallace's "Beginning Algebra Lab Notebook: GCF and Grouping - Grouping and Change Order"

Complete pages 76 and 77 of Wallace's workbook to practice with grouping and order change. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Tyler Wallace's "GCF and Grouping - Change Order"

Watch this five-minute video, paying attention to the examples being used to explain grouping with order change. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.

You may take different steps than in the video - or even more steps - but please make sure that you get the same result and that you understand the steps taken in the video.

4.1.5: Homework Assessment Tyler Wallace's "Beginning and Intermediate Algebra: Practice - Greatest Common Factor"

Answer every other odd-numbered problem for questions 1 through 31.

Tyler Wallace's "Beginning and Intermediate Algebra: Practice - Grouping"

Answer every other odd-numbered problem for questions 1 through 27.

4.2: Factoring Trinomials Tyler Wallace's "Beginning and Intermediate Algebra: Section 6.3: Factoring - Trinomials Where a = 1"

Read this section. Pay special attention to page 221.

This method of factoring (the ac method) really is the workhorse of factoring trinomials: We need two numbers whose product is the constant term and whose sum is the x coefficient.

4.2.1: Leading Coefficient Is 1 - Part 1 Tyler Wallace's "Beginning Algebra Lab Notebook: Trinomials - a = 1"

Complete page 80 of Wallace's workbook to practice with trinomials when a = 1. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Tyler Wallace's "Trinomials - a = 1" and MathIsPower4U's "Factor Trinomials when A equals 1"

Watch these videos, paying attention to the examples used to explain how to factor trinomials when a is equal to 1. You may watch the videos as often as you please. You may refer to the video when doing your homework, if necessary.

4.2.2: Leading Coefficient Is 1 with GCF - Part 2 Tyler Wallace's "Beginning Algebra Lab Notebook: Trinomials - a = 1 with GCF"

Complete page 81 of Wallace's workbook for more practice with trinomials when a = 1. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Tyler Wallace's "Trinomials - a = 1 with GCF"

Watch this four-minute video for a continuation of the video that explains how to factor trinomials when a is equal to 1.

4.2.3: Leading Coefficient Is Not 1 - Part 1 Tyler Wallace's "Beginning and Intermediate Algebra: Section 6.4: Factoring - Trinomials Where a ≠ 1"

Read this section. When we multiply polynomials we are distributing across parentheses. Here we are doing the reverse: We are trying to write a polynomial as a product of factors. We will introduce several techniques, and you should focus on learning them all because later it will be up to you to match the correct technique to a given problem.

Tyler Wallace's "Beginning Algebra Lab Notebook: Trinomials - a ≠ 1"

Complete page 78 of Wallace's workbook for practice with trinomials when a ≠ 1. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Tyler Wallace's "Trinomials - a ≠ 1 Part 1"

Watch this four-minute video. Pay attention to the examples used to describe how to factor trinomials when the leading coefficient is not 1. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.

4.2.4: Leading Coefficient Is Not 1 - Part 2 Tyler Wallace's "Trinomials - a ≠ 1 Part 2" and MathIsPower4U's "Factor Trinomials when A is NOT equal to 1 - Grouping Method"
Watch these videos, which demonstrate how trinomials can be factored when the leading coefficient is not 1.
4.2.5: Leading Coefficient Is Not 1 with GCF - Part 1 Tyler Wallace's "Beginning Algebra Lab Notebook: Trinomials - a ≠ 1 with GCF"

Complete page 79 of Wallace's workbook for more practice with trinomials when a ≠ 1. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Tyler Wallace's "Trinomials - a ≠ 1 with GCF Part 1"

Watch this four-minute video, paying attention to the examples being used to explain the concept in this unit.

4.2.6: Leading Coefficient Is Not 1 with GCF - Part 2 Tyler Wallace's "Trinomials - a ≠ 1 with GCF Part 2"

Watch this four-minute video. Pay attention to the examples being used to explain the concept in this unit. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.

4.2.7: Homework Assessment Tyler Wallace's "Beginning and Intermediate Algebra: "Practice - Trinomials Where a = 1"

Answer the odd-numbered problems 1 to 25.

Tyler Wallace's "Beginning and Intermediate Algebra: Practice - Trinomials Where a ≠ 1"

Answer the odd-numbered problems 1 to 39.

4.3: Special Products Tyler Wallace's "Beginning and Intermediate Algebra: Section 6.5: Factoring - Factoring Special Products"

Read this section. There is an error in Exercise 308 on page 231. You can find the correction in Saylor Academy's "Correction to Exercise 308, Page 231".

4.3.1: Difference of Squares Tyler Wallace's "Beginning Algebra Lab Notebook: Special Products - Difference of Squares"

Complete page 82 of Wallace's workbook to reinforce your understanding of differences of squares. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Tyler Wallace's "Special Products - Difference of Squares" and MathIsPower4U's "Factoring a Difference of Squares"

Watch these videos, which discuss the difference of squares.

4.3.2: Sum of Squares Tyler Wallace's "Beginning Algebra Lab Notebook: Special Products - Sum of Squares"

Complete page 83 of Wallace's workbook to reinforce your understanding of sum of squares. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Tyler Wallace's "Special Products - Sum of Squares"

Watch this two-minute video, which discusses the sum of squares. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.

4.3.3: Difference of 4th Powers Tyler Wallace's "Beginning Algebra Lab Notebook: Special Products - Difference of 4th Powers"

Complete page 84 of Wallace's workbook to reinforce your understanding the difference of 4th powers. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Tyler Wallace's "Special Products - Difference of 4th Powers"

Watch this four-minute video, which addresses how to use fourth powers. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.

4.3.4: Perfect Square Tyler Wallace's "Beginning Algebra Lab Notebook: Special Products - Perfect Squares"

Complete page 85 of Wallace's workbook for practice with perfect squares. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Tyler Wallace's "Special Products - Perfect Square" and MathIsPower4U's "Factoring a Perfect Square Trinomial"

Watch these videos, which discuss perfect squares and perfect square trinomials.

4.3.5: Cubes Tyler Wallace's "Beginning Algebra Lab Notebook: Special Products - Cubes"

Complete page 86 of Wallace's workbook to practice with cubes. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Tyler Wallace's "Special Products - Cubes" and MathIsPower4U's "Factoring a Sum or Difference of Cubes"

Watch these videos, which explain the concept of cubes.

4.3.6: GCF Tyler Wallace's "Beginning Algebra Lab Notebook: Special Products - GCF"

Complete page 87 of Wallace's workbook for practice with the greatest common factor in terms of special products. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Tyler Wallace's "Special Products - GCF"

Watch this three-minute video, paying attention to the examples being used to explain the concept of special products with the GCF. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.

4.3.7: Homework Assessment Tyler Wallace's "Beginning and Intermediate Algebra: Practice - Factoring Special Products"

Answer all of the odd-numbered problems for questions 1 through 47.

4.4.1: Strategy Tyler Wallace's "Beginning and Intermediate Algebra: Section 6.6: Factoring - Factoring Strategy"

Read this section. Pay special attention to page 234. Note that this reading corresponds to the workbook assignment at the end of this subunit.

Tyler Wallace's "Beginning Algebra Lab Notebook: Factoring Strategy - Strategy"

Complete page 88 of Wallace's workbook to reinforce your knowledge of when to use certain methods of factoring. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Tyler Wallace's "Factoring Strategy" and Bigbend Emporium's "Factoring Strategy"

Watch these videos, which discuss factoring strategies. You may watch the videos as often as you please. You may refer to the videos when doing your homework, if necessary.

4.4.2: Homework Assessment Tyler Wallace's "Beginning and Intermediate Algebra: Section 6.7: Factoring - Solve by Factoring"

Read this section. Here we emphasize how we can solve problems by factoring. Focus on the rule - "if ab = 0, then a = 0 or b = 0 (or both)" - and how factoring makes this rule so important.

4.5: Solve by Factoring Tyler Wallace's "Beginning and Intermediate Algebra: Section 6.7: Factoring - Solve by Factoring"

Read this section. Here we emphasize how we can solve problems by factoring. Focus on the rule - "if ab = 0, then a = 0 or b = 0 (or both)" - and how factoring makes this rule so important.

4.5.1: Zero Product Property Tyler Wallace's "Beginning Algebra Lab Notebook: Solve by Factoring - Zero Product Property"

Complete page 89 of Wallace's workbook to reinforce your knowledge of the zero product property. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Tyler Wallace's "Solve by Factoring - Zero Product Rule" and MathIsPower4U's "The Zero-Product Property" and "Solve an Equation in Factored Form"

Watch these videos, which explain the zero product rule.

4.5.2: Need to Factor Tyler Wallace's "Beginning Algebra Lab Notebook: Solve by Factoring - Need to Factor"

Complete page 90 of Wallace's workbook for practice with factoring. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Tyler Wallace's "Solve by Factoring - Need to Factor"

Watch this four-minute video. Pay attention to the examples to demonstrate how to solve by factoring.

4.5.3: Make Equal to Zero Tyler Wallace's "Beginning Algebra Lab Notebook: Solve by Factoring - Equal to Zero"

Complete page 91 of Wallace's workbook for practice with factoring. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Tyler Wallace's "Solve by Factoring - Make Equal to Zero"

Watch this five-minute video. Pay attention to the examples being used to explain how to factor by making the equation equal zero.

4.5.4: Simplifying Needed Tyler Wallace's "Beginning Algebra Lab Notebook: Solve by Factoring - Simplify"

Complete page 92 of Wallace's workbook for practice with simplifying and factoring. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Tyler Wallace's "Solve by Factoring - Simplify First"

Watch this five-minute video, focusing on the examples that discuss how to simplify equations. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.

4.5.5: Homework Assessment Tyler Wallace's "Beginning and Intermediate Algebra: Practice - Solve by Factoring"

Answer all of the odd-numbered problems for questions 1 through 35.

Unit 4 Practice Test Tyler Wallace's "Beginning and Intermediate Algebra: Unit 4 Practice Test"

Review Unit 4 before taking this practice test. Be sure that you are ready before taking the practice test, as it will give you a clear picture of what you know and the areas you need to review, if necessary. You may review the problems in the work pages in addition to watching the videos to prep for the practice test. When you have finished this practice test, you may check your answers against the "Unit 4 Practice Test - Answer Key".

5.1: Reduce Rational Expressions Tyler Wallace's "Beginning and Intermediate Algebra: Section 7.1 Rational Expressions - Reduce Rational Expressions"

Read this section. Rational expressions are just fractions and fractions of polynomials. Focus on the use of the rules of exponentiation and when we can cancel in fractions.

5.1.1: Evaluate Tyler Wallace's "Beginning Algebra Lab Notebook: Reduce - Evaluate"

Complete page 94 of Wallace's workbook for practice with reducing rational expressions. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Tyler Wallace's "Reduce - Evaluate"

Watch this four-minute video. Pay attention to the examples being used to explain evaluate rational expressions.

5.1.2: Reduce Fractions Tyler Wallace's "Beginning Algebra Lab Notebook: Reduce - Reduce Fractions"

Complete page 95 of Wallace's workbook for practice with reducing fractions. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Tyler Wallace's "Reduce - Reduce Fractions"

Watch this two-minute video. Pay attention to the examples being used to explain the concept of reducing fractions in rational expressions. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.

5.1.3: Reduce Monomials Tyler Wallace's "Beginning Algebra Lab Notebook: Reduce - Monomials"

Complete page 96 of Wallace's workbook for practice with reducing monomials. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Tyler Wallace's "Reduce - Monomials"

Watch these videos. Pay attention to the examples used to explain the concepts in this unit.

5.1.4: Reduce Polynomials Tyler Wallace's "Beginning Algebra Lab Notebook: Reduce - Polynomials"

Complete page 97 of Wallace's workbook for practice with reducing polynomials. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Tyler Wallace's "Reduce - Polynomials" and MathIsPower4U's "Simplify Rational Expressions"

Watch these videos, which discuss how to reduce polynomials.

5.1.5: Homework Assessment Tyler Wallace's "Beginning and Intermediate Algebra: Practice - Reduce Rational Expressions"

Answer all of the odd-numbered problems for questions 1 through 49.

5.2: Multiply & Divide Rational Expressions Tyler Wallace's "Beginning and Intermediate Algebra: Section 7.2: Rational Expression - Multiply & Divide"

Read this section. Again, rules for exponents are paramount, but now focus on dividing as "inverting and multiplying."

5.2.1: Multiply & Divide Fractions Tyler Wallace's "Beginning Algebra Lab Notebook: Multiply and Divide - Fractions"

Complete page 98 of Wallace's workbook for practice with multiplying and dividing fractions. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Tyler Wallace's "Multiply and Divide - Fractions" and MathIsPower4U's "Multiplication Involving Fractions"

Watch these videos, which show how to multiply and divide fractions.

5.2.2: Multiply & Divide Monomials Tyler Wallace's "Beginning Algebra Lab Notebook: Multiply and Divide - Monomials"

Complete page 99 of Wallace's workbook for practice with multiplying and dividing monomials. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Tyler Wallace's "Multiply and Divide - Monomials" and MathIsPower4U's "Multiply Rational Expressions - Monomials" and "Dividing Rational Expressions - Monomials"

Watch these videos, which discuss the multiplication and division of monomials.

5.2.3: Multiply & Divide Polynomials Tyler Wallace's "Beginning Algebra Lab Notebook: Multiply and Divide - Polynomials"

Complete page 100 of Wallace's workbook for practice with multiplying and dividing polynomials. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Tyler Wallace's "Beginning Algebra Lab Notebook: Multiply and Divide - Both at Once"

Complete page 101 of Wallace's workbook for practice with multiplying and dividing polynomials both at once. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Tyler Wallace's "Multiplying and Dividing Polynomials"

Watch these videos, which discuss the multiplication and division of polynomials. Remember that you may watch the videos as often as you please. You may refer to the video when doing your homework, if necessary.

MathIsPower4U's "Multiplying and Dividing Rational Expressions"

Watch these videos if you feel like you need additional help with this topic. These videos demonstrate how to solve variations on this kind of problem.

5.2.4: Homework Assessment Tyler Wallace's "Beginning and Intermediate Algebra: Practice - Multiply and Divide"

Answer all of the odd-numbered problems for questions 1 through 43.

5.3: Least Common Denominator (LCD) Tyler Wallace's "Beginning and Intermediate Algebra: Section 7.3: Rational Expressions - Least Common Denominators"

Read this section. One of the skills students have most difficulty with is adding fractions. You can make this much easier by understanding least common denominators.

5.3.1: Numbers Tyler Wallace's "Beginning Algebra Lab Notebook: LCD - Numbers"

Complete page 102 of Wallace's workbook for practice with the Lowest Common Denominator (LCD). Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Tyler Wallace's "LCD - Numbers" and MathIsPower4U's "Determining the Least Common Multiple Using a List of Multiples" and "Determining the Least Common Multiple Using Prime Factorization"

Watch these videos, which discuss the Least Common Denominator (LCD). You may watch the videos as often as you please. You may refer to the video when doing your homework, if necessary.

5.3.2: Monomials Tyler Wallace's "Beginning Algebra Lab Notebook: LCD - Monomials"

Complete page 103 of Wallace's workbook for more practice with Lowest Common Denominators. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Tyler Wallace's "LCD - Monomials" and Bigbend Emporium's "Least Common Multiple (LCM) with Variables"

Watch these videos, which discuss the Least Common Denominator with monomials.

5.3.3: Polynomials Tyler Wallace's "Beginning Algebra Lab Notebook: LCD - Polynomials"

Complete page 104 of Wallace's workbook for more practice with Lowest Common Denominators. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Tyler Wallace's "LCD - Polynomials"

Watch this five-minute video, which discusses the Least Common Denominator with polynomials.

5.3.4: Homework Assessment Tyler Wallace's "Beginning and Intermediate Algebra: Practice - Least Common Denominator"

Answer questions 11-20. If necessary, use the videos and information in this subunit to help you solve these problems.

5.4: Add & Subtract Rational Expressions Tyler Wallace's "Beginning and Intermediate Algebra: Section 7.4: Rational Expressions - Add & Subtract"

Read this section and complete the corresponding workbook assignment for this subunit. Notice that most of the work involves finding a common denominator; once that is done, we simply need to be careful with multiplication.

5.4.1: Add & Subtract Fractions Tyler Wallace's "Beginning Algebra Lab Notebook: Add and Subtract - Fractions"

Complete page 105 of Wallace's workbook for practice with adding and subtracting fractions. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Tyler Wallace's "Add and Subtract - Common Denominator"

Watch this five-minute video. Pay attention to the examples being used to explain how to add and subtract fractions.

5.4.2.1: Different Denominator - Part 1 Tyler Wallace's "Beginning and Intermediate Algebra: Section 7.5: Add and Subtract Rational Expressions: Different Denominator (Part 1)"

Read this section and complete the corresponding workbook assignment for the subunit.

Tyler Wallace's "Beginning Algebra Lab Notebook: Add and Subtract - Common Denominator"

Complete page 106 of Wallace's workbook for practice with adding and subtracting common denominators. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Tyler Wallace's "Add and Subtract - Different Denominators Part 1"

Watch this five-minute video. Pay attention to the examples used to explain adding and subtracting when there are different denominators. Here, one would first obtain a common denominator for the expressions involved and then proceed as in subunit 5.4.2.1 above.

5.4.2.2: Different Denominator - Part 2 Tyler Wallace's "Beginning Algebra Lab Notebook: Add and Subtract - Different Denominators"

Complete page 107 of Wallace's workbook for practice with adding and subtracting different denominators. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Tyler Wallace's "Add and Subtract - Different Denominators Part 2"

Watch this five-minute video which discusses adding and subtracting when there are different denominators. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.

5.4.3: Homework Assessment Tyler Wallace's "Beginning and Intermediate Algebra: Practice - Add and Subtract"

Answer the odd-numbered problems for questions 1 through 43.

5.5: Dimensional Analysis Tyler Wallace's "Beginning and Intermediate Algebra: Section 7.8: Rational Expressions - Dimensional Analysis"

Read this section and complete the corresponding workbook assignment for this subunit. Notice how converting from minutes to hours or feet to miles or cups to gallons all have the same foolproof method: canceling units of measurement.

5.5.1: Convert Single Unit Tyler Wallace's "Beginning Algebra Lab Notebook: Dimensional Analysis - Convert Single Unit"

Complete page 108 of Wallace's workbook for practice with dimensional analysis in which you convert single units. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Tyler Wallace's "Dimensional Analysis - Convert Single Unit"

Watch this five-minute video which discusses converting single units. You may watch the video as often as you please. You may refer to the video when doing your homework, if necessary.

5.5.2: Convert Dual Unit Tyler Wallace's "Beginning Algebra Lab Notebook: Dimensional Analysis - Convert Two Units"

Complete page 109 of Wallace's workbook for practice with dimensional analysis with converting dual units. Try to complete this exercise before watching the video in this subunit, and then review the worksheet as you follow along with the video for solutions.

Tyler Wallace's "Dimensional Analysis - Convert Two Units"

Watch this five-minute video, which discusses converting dual units.

5.5.3: Homework Assessment Tyler Wallace's "Beginning and Intermediate Algebra: Practice - Dimensional Analysis"

Unit 5 Practice Test Tyler Wallace's "Beginning and Intermediate Algebra: Unit 5 Practice Test"

Review Unit 5 before taking this practice test. Be sure that you are ready before taking the practice test, as it will give you a clear picture of what you know and the areas you need to review, if necessary. You may review the problems in the work pages in addition to watching the videos to prep for the practice test. When you have finished this practice test, you may check your answers against the "Unit 5 Practice Test - Answer Key".

Optional Course Evaluation Survey Optional Course Evaluation Survey

Please take a few moments to provide some feedback about this course. Consider completing the survey whether you have completed the course, you are nearly at that point, or you have just come to study one unit or a few units of this course.

Your feedback will focus our efforts to continually improve our course design, content, technology, and general ease-of-use. Additionally, your input will be considered alongside our consulting professors' evaluation of the course during its next round of peer review. As always, please report urgent course experience concerns to [email protected] and/or our discussion forums.

1.1: Order of Operations Introduction to Order of Operations

By convention, we use the order of operations to always perform operations in order that gives the same result each time. Mathematics would be useless if some people thought 3 + 4 x 2 = 14 and others thought 3 + 4 x 2 = 11! Understanding the order of operations is the most basic (and important) task of a student of mathematics.

Order of Operations

The primary rule for order of operations is that things in parentheses should be simplified first. Try to complete the practice problems before watching the videos. As you watch, pay attention to the order that operations follow (using the PEMDAS mnemonic, which stands for "parentheses, exponents, multiplication, division, addition, and subtraction").

Absolute Value

Absolute values tell us how far apart two numbers are. Absolute value lines, like parentheses, are a grouping symbol. This means that you have to perform operations inside the absolute value lines first, and then find the absolute value of the result. Try to complete the practice problems on your own before you watch the video.

Fractions

Fractions allow us to manipulate complicated expressions that include division. Being able to work with fractions allows us to simplify (and often avoid) division. A fraction line indicates division, but it also separates the operations on top from the operations on the bottom. Each side has to be performed separately first, and then you can divide. Try to complete the practice problems on your own before you watch the video.

1.2: Evaluating Algebraic Expressions Properties of Algebra

Evaluating algebraic expressions involves plugging in the given values for the variables, then using order of operations to calculate the result. This section covers how to evaluate algebraic expressions for some given values.

Evaluating Algebraic Expressions

These problems relate to how to evaluate expressions. Try to complete them on your own before you watch the video.

1.3: Simplifying Algebraic Expressions Combine Like Terms

To simplify algebraic expressions, you need to understand how to manipulate the terms with variables or combinations of variables. Terms containing exactly the same combinations of variables are called "like terms", and they can be combined by addition or subtraction. Try to complete the practice problems on your own before you watch the video.

The Distributive Property

More complex algebraic expressions contain parenthesis. To simplify these expressions, the parenthesis need to be removed. This can be done by using the distributive property of multiplication. When we distribute, we take the sign of the number we are distributing into consideration. If you distribute a negative number over a positive number, you get a negative number, and vice versa. Be careful when you distribute negative numbers. Try to complete the practice problems on your own before you watch the video.

Distribute and Combine

Now, we will distribute and combine like terms. The goal here is to be able to distribute (that is, remove parentheses) and then combine terms that are have the same variable or group of variables and exponents. Remember that combining like terms is simply adding or subtracting the numerical coefficients in the like terms. Try to complete the practice problems on your own before you watch the video.

1.4: Linear Equations in One Variable: One-Step and Two-Step Equations Solving One-Step Equations

Read this section to learn how to solve one-step equations.

One-Step Equations

In linear equations, we can add and multiply same expressions on both sides of the equation. We must do the same thing to each side to keep the equation balanced. Otherwise, we will change the equation to something that is different than what we started with, and we will not get the solution we are looking for. Try to complete the practice problems on your own before you watch the video.

Solving Two-Step Equations

Read this section to learn how to solve two-step equations.

Two-Step Equations

Try to complete the practice problems on your own before you watch the video.

Solving One- and Two-Step Equations

Watch these optional videos if you feel like you need more help with these topics.

1.5: Linear Equations in One Variable: General Equations Solving General Linear Equations

Now we will solve more complex linear equations, such as ones with variables on both sides, or ones that involve parentheses. These equations can be simplified and turned into the form of the two-step equations we have solved in the previous subunit. You will also learn special techniques for solving equations that contain fractional and decimal coefficients.

General Linear Equations

Here, we will practice simplifying general linear equations with one variable. Try to complete the practice problems on your own before you watch the video and read the solution.

Solving Fractions

Now, we will look at equations that contain fractions. Read this section and work through the examples. These equations could be solved by the same methods as any general equation, but "clearing" the fractions by multiplying the equation by Least Common Denominator speeds up the process.

Distributing with Fractions

Let's practice solving equations with fractions. Try to complete the practice problems on your own before you watch the videos.

Solving Linear Equations

Read this section and work through example 7. You can also try examples 14-18 in the "Topic Exercises" section if you'd like additional practice. The answers are found at the end of the section.

1.6: Linear Equations with Special Solutions Analyzing the Number of Solutions to Linear Equations

Linear equations in one variable do not always have one unique solution. Watch these videos to see how some equations have one solution, others have no solutions, and others have an infinite number of solutions.

1.7: Literal Equations and Formulas Solving Linear Equations - Formulas

Read this section. You now have the skills to solve a formula that relates two or more quantities for whichever quantity you want. This is an important algebra skill that we will use throughout the course. It is also used extensively in the sciences and in lots of other real-world applications.

Two-Step Formulas

Now, we will practice two-step formulas. Try to complete the practice problems on your own before you watch the video.

Manipulating Formulas

Watch these videos for step-by-step examples of how to manipulate perimeter and area formulas.

Multi-Step Formulas

Now, we will practice multi-step formulas. Try to complete the practice problems on your own before you watch the video.

Formulas with Fractions

Now, we will practice clearing fractions. Try to complete the practice problems on your own before you watch the videos, which demonstrate how to clear fractions and how to manipulate a formula that converts Fahrenheit to Celsius and vice versa.

1.8: Equations with Absolute Values Solving Linear Equations - Absolute Value

Read this section, which discusses how to solve the equations with an absolute value. The equations $x-3=2$ and $\left |x-3 \right |=2$ are very different from each other, but they are also closely related. Typically, an equation with absolute values will turn into two equations without absolute values.

Absolute Values with Two Solutions

It's time to practice absolute value equations with two solutions. Try to complete the practice problems on your own before you watch the video.

Isolate Absolute Values

Now, we'll practice equations by isolating absolute values. Do not break up the equation until you have isolated the absolute value. Try to complete the practice problems on your own before you watch the video.

Two Absolute Values

Here we'll take a look at equations with two absolute values. Try to complete the practice problems on your own before you watch the video.

1.9: Introduction to Word Problems: Translating English to Math Writing Expressions with Variables

Here, we will discuss how to turn word problems into algebraic equations, which will let us solve word problems using algebraic methods, which is a skill we will have to have for the later units in this course. Read this article, which explains why we have math if we can describe things in words.

Examples of Writing Expressions with Variables

These videos go over more examples of how to translate simple verbal expressions into algebraic equations, including those that contain more than one mathematical operation, and those that involve parentheses.

1.10: Number Problems and Consecutive Integer Problems Linear Equations - Number and Geometry

Word problems are about gathering information, turning it into equations, and then using the equations to solve the problem. Read this section and focus on the ways that we turn English statements into mathematical equations. Work through the examples of number and consecutive integer problems carefully.

Word Problems - Number Problems

Let's try solving number problems on our own. These problems relate to translating words into mathematical problems. Try to complete the practice problems on your own before you watch the video.

Word Problems - Consecutive Integers
Now we'll practice solving word problems with consecutive integers. Try to complete the practice problems on your own before you watch the video.
Word Problems - Consecutive Even/Odd

Think about how we express consecutive odd and even integers using one variable. Try to complete the practice problems on your own before you watch the video.

More on Sums of Consecutive Integers

If you want more practice with these kinds of problems, watch these videos, which give a step-by-step example of the sum of consecutive integers and the sum of consecutive odd integers.

1.11: Geometry Applications: Angles of Triangles and Perimeter Problems Word Problems - Triangles

Now we'll practice problems involving the angles of triangles. Try to complete the practice problems on your own before you watch the video.

Word Problems - Perimeter

Next, we'll do problems that involve perimeters of rectangles. Try to complete the practice problems on your own before you watch the video.

Applications of Linear Equations

This section reviews what we've looked at so far. Read it to see how well you understand how to solve word problems algebraically. Try Topic Exercises 1-44 for extra practice, and check your answers against those at the end of the section.

1.12: Age Problems Solving Linear Equations - Age Problems

Read this section and work through the examples. To solve these kinds of problems, organize the information given in the problem and translate it to algebraic expressions.

Age Problems - Variable Now

You will often encounter word problems like these that ask you to solve for a person's age. Try to complete the practice problems on your own before you watch the video.

More on Age Word Problems

Watch these optional videos if you'd like to see more examples of how to solve age problems.

Age Problems - Sum Now and Variable Time

Here are some word problems related to a person's age. Try to complete the practice problems on your own before you watch the video.

2.1: Graphing Points and Lines Graphing Point and Lines

One of our most powerful tools is visualization; graphs and X-Y coordinates are the foundation of "seeing" math. This section will help you get comfortable with working with points and lines in a coordinate system.

Two-Variable Linear Equations

Watch these videos, which explain how linear equations in two variables become a line when their solutions are plotted as points on a coordinate plane. In the second video, the equation is first rewritten so that $y$ is expressed in terms of $x$.

Graphing and Slope - Points and Lines

Let's practice creating graphs of points or from equations of a line. Try to complete the practice problems on your own before you watch the video.

2.2: Slopes, the Slope Formula, and Rate of Change Graphing Slopes

Read this section, which focuses on one fundamental property of the line: its slope. The slope tells us how much the line rises as we move to the right (that is, positively on the [\ x \]-axis). In other words, it indicates how steep the line is and whether the line rises or falls as it goes from left to right. Record the slope formula to refer to as you work through the examples in this section and the practice problems that follow.

Slope from a Graph

Now, let's practice determining the slope of a line given its graph. Try to complete the practice problems on your own before you watch the video.

Slope from Two Points

Now, we'll practice finding the slope when given two sets of points. Try to complete the practice problems on your own before you watch the video.

Rates of Change

When the equation of a line models the relationship between the two quantities in a real-life situation, its slope indicates how fast one quantity changes compared to the other. This physical meaning of the slope is usually referred to as the rate of change. Read this article to explore some examples of line that model real-life situations.

2.3: Intercepts of a Line and Horizontal and Vertical Lines x- and y- Intercepts

An intercept is a point where a line intersects the x- or y- axis. It is another important property of a line. Watch these videos to see how to intercepts from graphs or equations of lines.

Horizontal and Vertical Lines

These videos will help you understand how to determine the slope of horizontal and vertical lines, and how to write equations to represent them.

2.4: Slope-Intercept Form of a Linear Equation in Two Variables Graphing - Slope-Intercept Form

This section explores one way to write a linear equation in two variables: slope-intercept form. We will learn how to identify the slope and y-intercept of a line given in this form, graph these equations, and convert any linear equation to slope-intercept form.

Slope-Intercept Equations

Now, we'll practice slope-intercept equations. Try to complete the practice problems on your own before you watch the video.

Putting Equations in Slope-Intercept Form

It's time to practice putting an equation in slope-intercept form. Try to complete the practice problems on your own before you watch the video.

Graphing Equations

Here, we will use the slope and y-intercept to graph a line. Be sure that you understand the different parts of the straight line equation and the names that go with them. You may practice by graphing your own lines and seeing if you can label them completely. Try to complete the practice problems on your own before you watch the video.

Equations of Vertical and Horizontal Lines

Horizontal lines have a slope of 0, and vertical lines have an undefined slope. You can remember this by thinking of how vertical lines have an infinitely large slope, since they are infinitely steep. Because of this, horizontal and vertical lines have special equations that are easy to identify and to write. Try to complete the practice problems on your own before you watch the video.

2.5: Point-Slope Form of a Linear Equation in Two Variables Point-Slope Form

This section introduces point-slope form, which is another way to write linear equations in two variables. This form is convenient for writing equations when you know the slope and a point on the line other than the y-intercept.

Point-Slope Equations

Now we'll practice the point-slope form of an equation, given a point the line passes through and the slope of the line. Try to complete the practice problems on your own before you watch the video.