# Ch 6: Understanding, Solving & Graphing Inequalities

### About This Chapter

## Understanding, Solving & Graphing Inequalities - Chapter Summary

The lessons in this chapter help you understand, solve and graph inequalities and absolute value inequalities. You can also review a lesson on how to graph 1-variable inequalities. There are plenty of practice problems available in each lesson. After completing the chapter, you should be prepared to:

- Offer a clear definition for inequality
- Provide an overview of compound inequalities
- Explain how to solve radical inequalities
- Discuss the process of solving quadratic inequalities
- Graph 2-variable inequalities

Our experienced instructors use real-world examples to assist you with understanding, solving and graphing inequalities. The video lessons make learning fun and more interesting. You can study all of the lessons in the chapter or just a select few based on your specific needs. Each video lesson includes a written transcript that you can print and use to study offline.

### 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.

### 7. Graphing & Solving Quadratic Inequalities: Examples & Process

Graphing and solving quadratic inequalities is a process and an essential skill to be successful in many math subjects. Learn the definition of a quadratic inequality, how to plot points on a graph, explain the graph, and where to shade a graph.

### 8. Solving Radical Inequalities

This lesson will show how to solve radical inequalities using radical definitions and properties. Key terms and radical notes are included to share step by step the method to solve these special types of inequalities.

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### Other Chapters

Other chapters within the CLEP Precalculus: Study Guide & Test Prep course

- Functions
- Recognizing Functions
- Working with Exponential and Logarithmic Functions
- Piecewise and Composite Functions
- Functions as Models
- Understanding Linear and Nonlinear Equations
- Radical, Rational and Absolute Value Equations
- Parabolas, Ellipses and Hyperbolas
- Factoring & Solving Quadratic Equations
- Exponents and Polynomials
- Geometry and Trigonometry
- Using Scientific Calculators
- Trigonometry Overview
- CLEP Precalculus Flashcards
- Additional CLEP Precalculus Flashcards