5|x + 1| + 6 = 21
5|x + 1| = 15
|x + 1| = 3
Recall the definition of absolute value: |x| = +x if x ≥ 0, and |x| = -x if x < 0.
This means
- if x + 1 ≥ 0, or x ≥ -1, then |x + 1| = x + 1, and so
x + 1 = 3
x = 2, or
- if x + 1 < 0, or x < -1, then |x + 1| = -(x + 1), and so
-(x + 1) = 3
x + 1 = -3
x = -4
