# Ch 51: Inequalities Overview

### About This Chapter

## Inequalities Overview - Chapter Summary

Our instructors explain what a mathematical inequality is, followed by how to graph one- and two-variable inequalities. You will learn about set notation, systems of inequalities and compound inequalities. Practice problems follow that allow you to use the skills you've learned to graph inequalities.

Your study continues with an explanation of how to graph and solve an absolute value inequality, and practice problems are also provided. After you have reviewed this chapter, you will be able to:

- Define inequality
- Graph one-and two-variable inequalities
- Describe compound inequalities
- Solve graphing inequality problems
- Calculate absolute value inequalities

If you require assistance as you work through the lessons, contact one of our instructors for help. Our mobile-friendly lessons and quizzes are accessible to you at any time, seven days a week. You can use the quizzes and chapter tests to see how well you understand the material and where you may need to focus additional study.

### 1. What is an Inequality?

An inequality is an equation that uses greater or less than symbols and is helpful in situations with multiple solutions. Explore inequalities, two-variable inequalities, and how to graph two-variable inequalities.

### 2. How to Graph 1- and 2-Variable Inequalities

The number of variable inequalities in an equation affects how it is solved and graphed. Learn more about the properties of one-variable and two-variable inequalities and how to graph them on number lines and coordinate planes.

### 3. Set Notation, Compound Inequalities, and Systems of Inequalities

To solve problems where there are multiple points that require inequality symbols, strategies for compound equalities must be used. Learn about compound inequalities and how to represent these problems through set notation and interval notation and how to use systems of inequalities to solve these types of problems.

### 4. Graphing Inequalities: Practice Problems

Whether an inequality has one or two variables is an important distinction when graphing these types of algebraic expressions. Learn more about when to use a number line or a coordinate plane when graphing inequalities by solving some practice problems.

### 5. How to Solve and Graph an Absolute Value Inequality

Inequalities express 'greater than' or 'less than' and are useful in situations where the maximum or minimum is known and can be solved like equations. Learn the rules for solving and graphing inequalities with one variable and two variables, including absolute values.

### 6. Solving and Graphing Absolute Value Inequalities: Practice Problems

Absolute value inequalities must be split into new inequalities in order to be solved. Explore the difference between an AND and an OR compound inequality and how to solve and graph them using a system of inequalities with practice problems.

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