35 Test Page
Topic A. Solving Equations and Evaluating Expressions
Objectives:
- Use additional resources to practice algebra, as needed.
- Learn to check answers in some way other than looking “in the back of the book.”
- Use the distributive property and other properties to simplify algebraic expressions and check your work.
- Solve and simplify linear equations and check solutions of equations by plugging them back in.
- Solve equations with variables in the denominator and check solutions by plugging them in.
- Solve equations of those two types with multiple variables for one variable, resulting in a formula for that one variable.
- Evaluate variable expressions when given the value of each variable, using the correct order of operations.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Overview
The prerequisite for these materials includes mastery of basic math skills and some algebra, as needed to achieve “college-level” on Texas’ THEA test. Many students who have learned math at this level forget it easily, so this review section of some algebra is provided. Some students in the class will go through this material quickly and others will need to go much more slowly and do more review work. Additional optional practice problems are provided on the course web pages. The next few topics in the do not use this algebra, so it isn’t necessary to master everything in this topic immediately. It is necessary to master it before moving into Topic G (Linear Equations) and later.
A major difference between this course and most other math courses involves “checking your answer by looking in the back of the book.” In standard algebra classes, students practice quite a lot of similar problems and are expected to check many of the answers by looking in the back of the book. When we use mathematics in applications in the real world, there is no “back of the book.” In this course, we will learn methods for independently checking our results to see if they are correct, or at least reasonable, without having to rely on answers that someone else gives us. Most students find this awkward at first, but when they persist in practicing the checking methods, develop more confidence in using mathematics and in their problem-solving skills. There are not easy checking methods for all the techniques covered here, so some answers are provided. Generally, however, for particular topic, if you are expected to check your answer by an independent method, an answer key is not provided.
Section 1. Use the distributive property and other properties to simplify expressions and check your work.
Distributive Property:
For any real numbers a, b, and c: a(b + c) = ab + ac.
For any real numbers a, b, and c: a(b – c) = ab – ac
The fact that two expressions are equal means that they are equal for any values of the variable. So you can check by taking a few values for the variable and making sure that those do make the two sides equal. Usually we don’t use the values 0 or 1 or 2 as the