# Chapter 2: Linear Equations and Inequalities

## Introduction

Here you'll learn how to solve equations in one variable as well as inequalities in one variable. You will learn how to translate words into mathematical symbols in order to solve word problems using equations. You will also learn about absolute value and how to solve equations and inequalities that contain absolute value symbols. For inequalities, you will learn how to represent your solutions graphically on a number line.

## Chapter Outline

- 2.1. Equations with Variables on One Side
- 2.2. Equations with Variables on Both Sides
- 2.3. Equations with the Distributive Property
- 2.4. Equations with Decimals
- 2.5. Equations with Fractions
- 2.6. Equations with Decimals, Fractions and Parentheses
- 2.7. Mathematical Symbols to Represent Words
- 2.8. Algebraic Equations to Represent Words
- 2.9. One Variable Inequalities
- 2.10. Algebraic Solutions to One Variable Inequalities
- 2.11. Graphical Solutions to One Variable Inequalities
- 2.12. Absolute Value
- 2.13. Solutions to Absolute Value Equations
- 2.14. Algebraic Solutions to Absolute Value Inequalities
- 2.15. Graphical Solutions to Absolute Value Inequalities

### Chapter Summary

## Summary

You learned how to solve equations where variables were on one side of the equation, where variables were on both sides of the equation, and also when there were parentheses involved in the equations. The key to solving these equations was to make sure that whatever you did to one side of the equals sign, you did the other.

You learned how to translate from words into mathematical symbols in order to solve linear equations. Remember the key steps were to identify key words in the problem and from there write your linear equation. Sometimes it is helpful to circle mathematical operations and underline constants and variables to help you in the identification of key words.

Next you learned about one variable inequalities. Remember that inequalities do not have an equals sign but rather us the , and signs to relate the two mathematical expressions. The rules for solving inequalities remained the same as for equations with one exception. The exception was if you have to multiply or divide by a negative number. If this happens, you have to reverse the sign of the inequality.

You learned to graph inequalities on a real number line. You used an open circle for > and <. You used a closed circle for and .

Finally, you were introduced to absolute value. In solving with absolute value, for both equations and inequalities, the rules remain the same with one addition. Because you are dealing with the absolute value function, you have to solve for the two related expressions when solving an equation or inequality.