The solution of the inequality is (x > - 8 and x < 2) or (x > 6 and x < 16).
How to find the solution set of an inequality
Herein we find an inequality that involves two absolute values. Absolute values are defined by the following piecewise functions:
- |x - a| = x - a for x ≥ a
- |x - a| = - x + a for x < a
Now we proceed to solve the inequality given:
||x - 4| - 7| < 5
- 5 < |x - 4| - 7 < 5
0 < |x - 4| - 2 < 10
|x - 4| - 2 > 0 and |x - 4| - 2 < 10
Case 1: |x - 4| - 2 > 0
|x - 4| > 2
x - 4 > 2 and x - 4 < - 2
x > 6 and x < 2
Case 2: |x - 4| - 2 < 10
|x - 4| < 12
x - 4 < 12 and x - 4 > - 12
x < 16 and x > - 8
The solution of the inequality is (x > - 8 and x < 2) or (x > 6 and x < 16).
To learn more on inequalities: https://brainly.com/question/20383699
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