<img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />
Dismiss
Skip Navigation
Our Terms of Use (click here to view) have changed. By continuing to use this site, you are agreeing to our new Terms of Use.

6.6: Absolute Value Inequalities

Difficulty Level: At Grade Created by: CK-12
Turn In

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.

|x|10.

Solution: |x|10 represents all numbers whose distance from the origin is less than or equal to 10. This means that 10x10.

b. Solve the inequality.

|x|10.

Solution: |x|10 represents all numbers whose distance from the origin is greater than or equal to 10. This means that x10 or x10.

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 |x|<aa<x<a and |x|>ax<a or x>a.

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

Error Troubleshooting

NONE

Notes/Highlights Having trouble? Report an issue.

Color Highlighted Text Notes
Show More

Image Attributions

Show Hide Details
Files can only be attached to the latest version of section
Please wait...
Please wait...
Image Detail
Sizes: Medium | Original
 
CK.MAT.ENG.TE.1.Algebra-I.6.6
Here