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6.6: Absolute Value Inequalities

Difficulty Level: At Grade Created by: CK-12
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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.

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CK.MAT.ENG.TE.1.Algebra-I.6.6