RWM102: Algebra

Read these notes to get a handle on the definitions we'll be using and to see a few examples. After you read, complete a few practice problems and check your answers.

Watch this video, which highlights some common ways to write multiplication in algebra. It also shows examples of how to substitute values in algebraic expressions.

After you watch, complete these assessments that involve substituting values into algebraic expressions with variables. If you need help, use the review tools at the bottom of the page.

Continue with this second set of assessments. If you need help, use the review tools at the bottom of the page.

Watch this video to review the rules for order of operations. Many use the acronym PEMDAS to remember the order of operations: parentheses, exponents, multiplication and division, addition and subtraction.

Try each of the examples on this worksheet without looking at the solution. Then, check your answers. If you need more practice, you can do the review problems that follow the examples.

Watch these videos for examples of how to apply these laws in arithmetic.

Watch these videos for examples of how to use this property in arithmetic.

Watch this video for examples of how to use this property in arithmetic.

Review this brief definition and examples in this encyclopedia entry.

After you watch, complete this first set of assessments. If you need help, use the review tools at the bottom of the page.

Continue with this second set of assessments. If you need help, use the review tools at the bottom of the page.

Read the "Define Linear Equations in One Variable" and "Solutions to Linear Equations in One Variable" sections. Then, complete exercises 1 to 5 and check your answers.

Read up to the "Solve Equations that Require Simplification" section. Pay attention to the "Solve Equations Using the Subtraction and Addition Properties of Equality" section, which gives a good example of how the two sides of an equation must be equal. After you read, complete examples 2.2 through 2.5 and check your answers.

Read up to the "Sole Equations that Require Simplification" section. Complete examples 2.13 to 2.17.

Watch this video for examples of these types of equations.

After you watch, complete this assessment to test yourself.

After you watch, complete this assessment and check your answers.

Watch this video for examples of how to solve these types of problems in a two-step process.

After you watch, complete this assessment and check your answers.

Watch these videos to see examples of how we use like terms to solve these types of equations.

After you watch, complete this assessment and check your answers.

Watch these videos to see examples of how this type of equation can be solved.

After you watch, complete this assessment and check your answers.

Read the section on linear literal equations. Be sure to go through the examples in detail. After read, complete the exercises for literal equations and check your answers.

We can apply these concepts to known formulas, such as formulas for area of a shape or rates.

Watch these videos for real examples of using formulas. In the first video, the formula for perimeter of a rectangle is solved for the width. In the second, a formula is used to convert between Fahrenheit and Celsius.

Read this page. Pay close attention to the mathematical dictionary table. It may be helpful to copy this table so you can use it as a reference as you become more comfortable working with word problems.

Read through sample sets A and B to see how the word problems are translated into equations. After you read, complete practice sets A and B and check your answers.

Watch these videos which provide step-by-step examples of how to translate word problems into equations we can solve.

Read the five step method section, which outlines a way to organize your thinking and solve number problems. Note the five steps that set up the equation for a word problem. Then, read the first two examples in sample set A. These examples show how to use the five step method to set up and solve number problems. Finally, do the first two problems in practice set A and check your answers.

Watch these videos. The first shows word problems involving consecutive integers. The second shows a more challenging problem involving the sum of odd integers. When summing odd integers, the equation must be slightly altered.

Read the discussion on consecutive integers, which shows how to write consecutive integers or consecutive even or odd integers. After you read, complete questions 3 and 4 in practice set A and check your answers.

Watch this video for examples of these types of problems. Recall the five step method we discussed in section 3.3. When you solve these types of problems, the first key step is to identify the variable.

Read this article for another example of this type of a general statement problem. In this problem, it looks like there are two variables. However, we can relate the quantity of one variable to that of the other. This allows us to write the equation in terms of only one variable.

At the bottom of the page, try a few practice problems and check your answers. Try a couple of these until you feel comfortable writing and solving equations from general word problems.

Read the section on the distance, rate, and time formula. We use this equation for all uniform motion problems. Then, do examples 2.58 through 2.60 and check your answers. If you want more practice, you can try exercises 376 and 387.

Watch this video for examples of how to express a mixture problem in an algebraic equation.

Then, watch these videos to see more examples of how to write and solve these types of problems.

After you watch, complete examples 3.26 through 3.32 and check your answers.

Read this section for examples of how to calculate percent from fractions, and how to translate a percent word problems into equations. Pay attention to the formula for finding the percent of change, since we use this formula frequently to determine sale prices.

After you read, complete this assessment and check your answers to practice solving problems with percents.

Read the section on inequalities, which shows the symbols used to denote greater than and less than. You must be able to quickly recognize these two symbols. Do example 1.12 and check your answer.

Watch this video.

Read these notes for more examples of how to plot inequalities.

Watch this video for examples of how to work with inequalities.

Then, watch this video to see examples of how inequalities are used in real world examples.

After you watch, complete this assessment and check your answers.

Watch these three videos.

After you watch, complete this assessment and check your answers.

Read this page and watch the videos in the text. Pay attention to the example near the end of the page and how the author identifies points that do not directly match up with the tick marks on the graph.

In this video, we see that if we graph an equation, the solutions must lie on the graph. This gives us an additional way to test if an ordered pair of numbers is a solution to an equation.

After you watch, complete this assessment and choose to solve the equations using algebra or graphs.

Watch these videos, which explain how to manipulate an equation into a format that allows for graphing.

Read this section to learn how to identify intercepts and how to use them in graphing and the general form of x- and y-intercepts.

After you read, complete examples 4.19 through 4.24.

Read this section. Pay attention to the definition of slope and how we define positive and negative slope. Also, pay attention to the slope formula given toward the end of the page. The slope formula will allow you to calculate the slope of any given line.

After you read, complete examples 4.25, 4.26, and 4.29 through 4.37 and check your work.

Read this page to see the special relationship of the slopes of parallel and perpendicular lines. After you read, try a few practice problems.

Read up to the section on choosing the most convenient method to graph a line. The form y = mx + b is often called the slope-intercept form of a linear equation.

After you read, complete examples 4.40 through 4.46 and check your work.

Read this page, which describes writing and graphing equations in point-slope and shows how to convert from the point-slope form to slope-intercept form, which can often be more useful. Watch the videos for more examples.

After you read, complete review problems 3, 4, 7, 8, 14, and 15 and check your answers.

Read this page, which reviews some calculations with inequalities and shows how we use shading on a graph to indicate inequality. Pay attention to the summary of graphing inequalities.

Complete examples 4.70 to 4.75 and check your answers.

Watch this video to see examples of how we apply algebra techniques to testing solutions to systems of equations.

Read this page, starting at the section on solving a system of linear equations by graphing. After you read, complete examples 5.3 through 5.7 and check your answers. You should use graph paper for these examples, since you will need to identify the intersection point between two lines.

Watch this video to see examples of using the substitution method.

After you watch, complete this assessment and check your answers.

Watch these videos for examples of how to solve systems of equations with the elimination method using a few different methods.

After you watch, complete this assessment and check your answers.

Read this article and watch the videos. The beginning provides a nice summary of the main methods for solving systems of equations, and when you should use each one. The rest of the article offers a good overview of the different methods with a discussion of why each method was chosen for a given problem.

Watch this video for examples of common real-world word problems.

Read this article and watch the video. The article describes examples in which systems of equations can be used to solve real-world quantities. After you review, complete problems 1 to 4 and check your answers.

Read this article and watch the video. The article describes examples in which systems of equations can be used to solve real-world quantities. After you review, complete problems 1 to 4 and check your answers.

Read this page until the section Solve Applications of Linear Inequalities. Pay attention to the steps needed to solve a system of linear inequalities.

After you read, complete examples 5.51 through 5.56 and check your answers.

Read the section on solving applications of linear inequalities. Review the examples to see how the authors use systems of linear inequalities to solve problems involving cost of objects and budgets.

Linear programming uses a system of several linear inequalities to analyze a real-world situation. Linear programming takes a set of inequalities and determines the optimal or best solution for the given set of conditions. Read this article to learn about this application of linear inequalities.

Read this article through the section on the product of powers property. This page reviews writing and solving exponential expressions. Pay attention to how we multiply monomials with exponents, the products of powers property, and example 2.

After you read, complete questions 2, 3, 6, 7, 8, 25, 26, 27 and 28 in the practice set and check your answers.

Read this article, which shows the rules for multiplying exponents, taking the power of an exponent, and taking the exponent of a product. It may help to write a list of these properties to keep track of them. Watch the video to see a few examples.

After you read, complete questions 2, 3, 6, 7, 14, 15, 25, 26, 33, and 34 in the practice set and check your answers.

Read this article and pay attention to the quotient of powers property and the power of a quotient property in examples 1 and 2.

After you read, complete questions 1, 2, 5, 6, 12, and 13 in the practice set and check your answers.

Watch these videos, which walk you through the logic of why negative exponents can be written as fractions.

After you watch, complete this assessment and check your answers.

Read the section on multiplying monomials and the solution for example 6.26.

After you read, complete example 6.27 and check your answer.

This article gives an excellent review of the properties of monomials and exponents, as well as how to divide monomials. Review the summary of exponent properties, which goes over everything we discussed in this unit.

After you read, complete examples 6.72 through 6.75 and check your work.

Watch this video to review the terminology we will use in this unit.

Read this page, which reviews how to classify polynomials. Pay attention to the section on adding and subtracting polynomials. You can rearrange the order of terms in a polynomial to make addition or subtraction possible. Read example 6.7 and its solution to see an example of adding polynomials. 

After you review, complete examples 6.8 to 6.12 and check your work.

Watch these videos for more examples of adding and subtracting polynomials.

Read this article and watch the videos. It may be helpful to review the section on multiplying monomials. Then, focus on how to use the distributive property and the examples of using it.

After you review, complete review problems 6 to 11 and check your answers.

Read this article, which gives many examples of using the FOIL technique to multiply two binomials. Then, try some practice problems.

Watch this video, which gives another example of using the FOIL technique.

Watch this video, which takes square of a binomial in two different ways: using the FOIL method and the quadratic formula. Both methods give the same answer.

Read this article, which gives examples of squaring binomials and the general formulas that always work for them. Example 1 shows how to use the formula. Note the definitions of sum and difference, which are used when multiplying one addition binomial and one subtraction binomial. Example 2 shows how to use this definition.

After you read, complete questions 1 through 5 and 14 through 18 in the practice set and check your answers.

Watch this video, which shows a method for ensuring that all terms in the polynomial (in this case a trinomial) are multiplied by both of the terms in the binomial using the distributive property.

Read the section on multiplying a trinomial by a binomial. Review the solution to example 6.45 to see how the distributive property can be used to multiply.

After you read, complete exercises 267, 269, 271, and 273 and check your answers.

Watch this example of dividing a polynomial by a monomial. This video gives an example of the technique we use to divide.

Read the section on dividing a polynomial by a monomial. Review the solutions for examples 6.77 and 6.78, which show how to divide a polynomial by a number and by a monomial.

After you read, complete examples 6.79 to 6.83 and check your answers.

Read the section on dividing a polynomial by a binomial. Pay attention to the review of long division, since it will help you understand the technique. Review the solution to example 6.84 to see how to divide a trinomial by a binomial. Then, review the solution to example 6.85 to see how we handle dividing by a subtraction binomial. Be careful, and make sure you keep track of the negative sign.

After you study these examples, complete questions 6.167 through 6.170 in the Try It section.

Read the section on dividing a polynomial by a binomial. Pay attention to the review of long division, since it will help you understand the technique. Review the solution to example 6.84 to see how to divide a trinomial by a binomial. Then, review the solution to example 6.85 to see how we handle dividing by a subtraction binomial. Be careful, and make sure you keep track of the negative sign.

After you study these examples, complete questions 6.167 through 6.170 in the Try It section.

Read this short article which provides an overview of the language and definitions you need to understand for factoring.

Read this page up to the section on factoring by grouping. Factoring takes advantage of the distributive property in the opposite way from how we did it in Unit 8.

After you read, complete examples 7.1 through 7.7 and check your work.

Watch the first six minutes of this video.

Work through example 3 in the section on factoring by grouping, and solve problems 11 to 15, 17, 18, and 23 through 27 in the practice set. All of these problems are four-term polynomials that you can factor by grouping. After you complete the practice problems, check your answers.

Read this article. The section Key Tools for Factoring Trinomials gives a brief overview of how factoring works, and Key Ideas for Finding the Numbers that Work also gives some basic rules to keep in mind when factoring.

Watch this video for an example of factoring a polynomial in this form.

After you watch, complete this assessment and check your answers.

Read this article. Pay attention to the overview of the steps for these problems. Read the examples and note where factoring is not possible, like in the last example. After you have reviewed the materials, complete a few practice problems until you feel comfortable. Be sure to check your answers when you are done.

Watch these two videos which go through examples of using the factoring by grouping method.

After you have watched the videos, complete this assignment and check your answers.

Watch these videos, which demonstrate different methods for factoring trinomials with two variables.

After you have watched the three videos, complete this assignment and check your answers.

Read this article up to the section on solving quadratic polynomial equations by factoring. Watch the videos and work through the guided practice examples.

After you review, complete practice problems 1 through 8 and check your answers.

This video shows how to check whether the given trinomial is a complete square. Factor it if it is. You should try to factor by grouping if it is not.

Read this article, which reviews the sum, difference, and square of the binomial equations we discussed earlier. Make sure you are comfortable with this before moving on. Pay attention to the examples of factoring the difference of two squares, since they show how to use the method.

After you read, complete review questions 1 through 5 and check your answers.

Watch this video to see an example of how we treat this special case of factoring.

Watch these videos. Factoring a trinomial requires two steps. First, a common monomial factor is factored out, and then the resulting polynomial is factored by grouping. The second video gives an example of a multi-step factoring process by factoring out a common monomial and then using the difference of cubes formula.

This article gives more examples and introduces the idea of "prime polynomials" that cannot be factored.

Complete this assignment and check your answers.

Read the section on solving quadratic equations using the zero product property. Review the solution to example 7.69 to see the steps for using the principle of zero product.

After you read, complete examples 7.70 and 7.71 and check your answers.

Read these two articles, which give examples of how factoring is used to solve quadratic equations. Try to identify the factoring methods being used and why each step is performed. After you have reviewed the materials, complete a few practice problems and check your answers.

Read each example slowly and try to identify the factoring methods being used and why each step is performed. After you have reviewed the materials, complete a few practice problems and check your answers.

Read this article, which shows how we use factoring in geometry and in problems where we need to find an unknown value.

After you read, complete review questions 1, 2, 5, 7, and 9 and check your answers.