Question

Solve: |x - 3| < 8

Answer 1

X is any number greater than -5 but less than 11
|x-3| < 8 (rewrite the equation to get read of the absolution)
-8 < x-3 < 8 (add three to both sides of the inequality to get x)
-5 < x < 11

If we substitute any number between -5 and 11 we see this is true
|x-3| < 8 if x = -4 or |x-3| < 8 if x = 10
|-4-3| < 8 ― |10-3| < 8
|-7| < 8 ― |7| < 8
7 < 8 (true) ― 7<8 (true)