Question

What is the solution to 9|x – 8| < 36?

4 < x < 12
x < –4 or x > 12
x > –12 or x < 8
–4 < x < 8

Answer 1

4 < x < 12

Explanation:

x - 8 ≥ 0

x ≥ 8

If x ≥ 8

9(x-8) < 36

9x - 72 < 36

9x < 36 + 72

9x < 108

9/9 x < 108/9

x < 12

8 ≤ x < 12

if x < 8

9(-x+8) < 36

-9x + 72 < 36

-9x < 36 - 72

-9x < -36

-9/-9 x > -36/-9

x > 4

4 < x < 8

4<x<12