Question

Solve 4\left| {x + 5} \right| + 8 = 244∣x+5∣+8=24.

Answer 1

Isolate the absolute value term:

4 |x + 5| + 8 = 24

4 |x + 5| = 16

|x + 5| = 4

By definition of absolute value,

• if x + 5 ≥ 0, then |x + 5| = x + 5, and so

x + 5 = 4

x = -1

• otherwise, if x + 5 < 0, then |x + 5| = -(x + 5), and so

-x - 5 = 4

-x = 9

x = -9