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.
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.
a. Solve the inequality.
Solution: |x|≤10 represents all numbers whose distance from the origin is less than or equal to 10. This means that −10≤x≤10.
b. Solve the inequality.
Solution: |x|≥10 represents all numbers whose distance from the origin is greater than or equal to 10. This means that x≤−10 or x≥10.
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|<a⇔−a<x<a and |x|>a⇔x<−a or x>a.
In Problems 4 and 5 in the Review Questions, have students divide by the coefficient of x first.