# Chapter 6: Linear Inequalities

**At Grade**Created by: CK-12

## Introduction

You’ve learned how to solve equations for a specific value, but what if the solution you were looking for involved a set of many answers. For example, you can pass a math test with any grade that is at least 65. Also, anyone under the age of 55 does not qualify for a senior discount. Both of these situations have many values that make them true statements, and inequalities are what you will use and solve to represent scenarios like these.

## Chapter Outline

- 6.1. Inequality Expressions
- 6.2. Linear Inequalities
- 6.3. Multi-Step Inequalities
- 6.4. Applications with Inequalities
- 6.5. Compound Inequalities
- 6.6. Solutions to Compound Inequalities
- 6.7. Absolute Value
- 6.8. Absolute Value Equations
- 6.9. Graphs of Absolute Value Equations
- 6.10. Absolute Value Inequalities
- 6.11. Graphs of Inequalities in One Variable
- 6.12. Linear Inequalities in Two Variables

### Chapter Summary

## Summary

To help you visualize inequalities, this chapter begins with graphing them on a number line. It then moves into solving inequalities that entail one and multiple operation(s) to isolate the variable. Next, writing, graphing, and solving compound inequalities are introduced. From there, the chapter transitions into absolute value equations and inequalities, with special attention paid to analysis and graphing of them. It concludes with graphing of linear inequalities in two variables and solving real-world problems using linear inequalities.