Chapter 2 / REVIEW Linear Equations and Inequalities in One Variable What’s the big idea? Chapter 2 provides us with the skills to solve equations and inequalities in one variable. Knowing how to solve these equations and inequalities gives us the foundation we need to solve some word problems. The properties that enable us to solve these types of problems also provide the framework for us to solve more difficult equations, which will be encountered in later chapters. The Tools Study Tips Listed below are the key terms, skills, formulas, and properties you should know for this chapter. The page reference is provided if you need additional help with the given topic. The Study Tips will assist in your preparation for an exam. 1. Learn all of the terms, formulas, and properties. Make flash cards and have someone quiz you. 2. Rework problems from the exercises and also the ones you worked in class. Work additional problems from the review exercises. 3. Review the summaries of key concepts. 4. Work the chapter test. 5. Be sure to review the online resources for additional study materials. Formulas and Properties • Addition property of equality 102 • Addition property of inequality 169 • Discount problem 152 • Distance formula 159 • General percent problem 151 • Markup problem 152 • Multiplication property of equality 112 • Multiplication property of inequality 169 • Percent increase or decrease 152 • Simple interest formula 154 Terms Area 137 Circumference 137 Complementary angles 142 Compound inequality 167 Conditional equation 129 Consecutive even integers 119 Consecutive integers 118 Consecutive odd integers 119 Contradictions 130 Equation 92 Equivalent equations 102 Expression 92 Formula 136 Identity 131 Interest 154 Interval notation 167 Linear equation in one variable 101 Linear inequality in one variable 166 Opposite angles 144 Perimeter 137 Right angle 142 Set-builder notation 168 Simple inequality 167 Solution of a linear inequality 166 Solution of the equation 92 Straight angle 142 Supplementary angles 142 Triangle 145 Vertical angles 144 CHAPTER 2 / SUMMARY How well do you know this chapter? Complete the following questions to find out. Take a look back at the section if you need help. SECTION 2.1 Equations and Their Solutions 1. A(n) is a statement in which two expressions are equal. 2. A(n) is a value of the variable that makes the equation true. 3. When translating phrases, the expressions , , , , and represent the equals sign. 183
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