# Ch 6: Absolute Value Equations & Inequalities

### About This Chapter

## Absolute Value Equations and Inequalities - Chapter Summary and Learning Objectives

Absolute value is the size, or magnitude, of a number, regardless of whether it is negative or positive. In these lessons, you'll learn to evaluate absolute value expressions and solve problems involving absolute value. Other lessons in this chapter cover graphs and transformations involving absolute value. This chapter can help you understand the following:

- Definition of an absolute value
- Absolute value expressions
- Absolute value equations
- Absolute value inequalities
- Graphing absolute value equations
- Graphing absolute value inequalities

Video | Objective |
---|---|

What Is an Absolute Value? | Define an absolute value |

How to Evaluate Absolute Value Expressions | Learn that the end value is always positive in an absolute value expression. |

How to Solve an Absolute Value Equation | Learn to split operations before solving for the variable. |

Solving Absolute Value Practice Problems | Gain practice in working with absolute value problems. |

How to Graph an Absolute Value and Do Transformations | Create a 'V'- shaped graph of an absolute value and use transformations to move the graph and change its appearance through translations. |

Graphing Absolute Value Equations: Dilations and Reflections | Learn to move the graph on the coordinate plane without changing its size. |

How to Solve and Graph an Absolute Value Inequality | Solve problems dealing with inequalities and learn to graph them. |

Solving and Graphing Absolute Value Inequalities: Practice Problems | Gain skill through problem-solving practice. |

### 1. What is an Absolute Value?

When we're talking and comparing numbers, we often don't care whether its positive or negative, just how big it is. This is often called the magnitude of a number and we find it by taking the absolute value. Learn all about it here!

### 2. How to Evaluate Absolute Value Expressions

Substituting values into absolute values doesn't have to be too hard, but it can be if you're given deceiving beginning information. See if you're up to it by checking out this video!

### 3. How to Solve an Absolute Value Equation

Once you get familiar with any new operation, the next step in any algebra class is to learn how to solve equations with that operation in them. Absolute values are no different. Solve absolute value equations here!

### 4. Solving Absolute Value Practice Problems

There are many easy mistakes to make when solving absolute value equations. Learn how to avoid those mistakes here by working on examples of absolute value equations with operations on the inside and the outside of the absolute value.

### 5. How to Graph an Absolute Value and Do Transformations

Absolute value graphs normally look like the letter 'V', but transformations can change that 'V' in a number of different ways. As well as teaching you how to graph absolute values, this video will focus on a specific group of transformations called translations. Learn all about what that means here!

### 6. Graphing Absolute Value Equations: Dilations & Reflections

Although a basic absolute value graph isn't complicated, transformations can make them sufficiently confusing! In this lesson, you'll practice different transformations of absolute value graphs.

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

Taking two skills and combining them to make a more complicated problem is a classic tactic in mathematics. If you feel confident with absolute values and inequalities, see if you can tackle them with their powers combined here!

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

Solving and graphing absolute value inequalities brings a lot of different skills together in one place. The practice problems in this video will give you a good chance to see more examples of absolute value inequalities but will also test your general algebraic knowledge.

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### Other Chapters

Other chapters within the Math 105: Precalculus Algebra course

- Mathematical Modeling
- Linear Equations & Inequalities
- Quadratic Functions
- Rational Expressions and Functions
- Polynomial Functions of a Higher Degree
- Complex Numbers
- Geometry Basics
- Functions Overview
- Function Operations
- Graph Symmetry
- Exponential and Logarithmic Functions
- Introduction to the Derivative
- Studying for Math 105