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: 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.