# 6.6: Absolute Value Inequalities

## Learning Objectives

At the end of this lesson, students will be able to:

- Solve absolute value inequalities.
- Rewrite and solve absolute value inequalities as compound inequalities.
- Solve real-world problems using absolute value inequalities.

## Vocabulary

Terms introduced in this lesson:

- absolute value inequality

## Teaching Strategies and Tips

Use Example 1 to show that the distance interpretation equally applies to absolute value *inequalities*.

Additional Examples:

a. *Solve the inequality.*

Solution: represents all numbers whose distance from the origin is *less than or equal to* . This means that .

b. *Solve the inequality.*

Solution: represents all numbers whose distance from the origin is *greater than or equal* to . This means that or .

Use Example 1 and the distance interpretation to motivate solving the absolute value inequalities in Examples 2-5.

- Allow students to infer from Example 1 that and or .

In Problems 4 and 5 in the *Review Questions*, have students divide by the coefficient of first.

## Error Troubleshooting

NONE