Unit 1: Basic Algebra Concepts
We begin by quickly reviewing the basic concepts you will need to understand as you begin your study of algebra. If you have taken a pre-algebra course, you may be familiar with some of these concepts. With practice, every student, regardless of background, can grasp these concepts.
Completing this unit should take you approximately 26 hours.
Upon successful completion of this unit, you will be able to:
- evaluate order of operations with absolute value;
- distribute and combine like terms;
- evaluate algebraic expressions;
- solve linear equations (simple, dual side variables, infinite or no solution, and rational coefficients);
- solve linear absolute value equations (simple and dual side);
- solve algebraic formulas with several variables for one of the variables; and
- solve applications of linear equations (age, integers, and triangles).
1.1: 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
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.
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
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.
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
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.
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
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
Read this section to learn how to evaluate algebraic expressions for some given values.
1.2.1: Evaluate Expressions
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.
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
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.
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
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.
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
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.
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
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: Linear Equations in One Variable
1.3.1: Equality Property of Addition and Multiplication
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
Read this section, beginning on page 28, to learn how to solve "one step equations."
Complete page 12 of Wallace's workbook for practice with solving one step linear equations.
1.3.3: Solving 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.
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.
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.
Watch this brief optional video if you feel like you need additional help with this topic.
1.3.4: Solving General Linear Equations in One Variable
Read this section, beginning on page 37, to learn how to solve general linear equations.
Watch this brief optional video if you feel like you need additional help with this topic.
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.
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
Read this section, beginning on page 43, to learn how to solve equations involving 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.
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.
Watch these brief optional videos if you feel like you need additional help with this topic.
1.3.6: Homework Assessment
Answer every other odd-numbered problem in questions 1 through 39.
Answer every other odd-numbered problem in questions 1 through 49.
Answer every other odd-numbered problem in questions 1 through 29.
1.4: Formulas
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
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.
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
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.
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
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.
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
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
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
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.
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
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).
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
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.
Complete page 22 of Wallace's workbook to practice solving for variables with equations that contain two absolute values.
1.5.4: Homework Assessment
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)
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
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.
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
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.
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
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.
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
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.
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
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.
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
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: Further Application Problems
1.7.1: Variable Age 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.
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.
Watch these brief optional videos if you feel like you need additional help with this topic.
1.7.2: Given Sum Ages 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.
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.
Watch this brief optional video if you feel like you need additional help with this topic.
1.7.3: Homework Assessment
Answer the odd numbered problems for questions 1 to 39. Solutions are on page 4 of the PDF.
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".
Unit 1 Assessment
Take this assessment to see how well you understood this unit.
- This assessment does not count towards your grade. It is just for practice!
- You will see the correct answers when you submit your answers. Use this to help you study for the final exam!
- You can take this assessment as many times as you want, whenever you want.