Question

What is the solution set for |–2x + 16| – 9 = –3

Answer 1

First, isolate the absolute value operation:
|–2x + 16| = 6
Simplify:
|8 - x| = 3

Now, break this into the two cases of an absolute value operation:
CASE 1: 8 - x >= 0, so we can simply remove the absolute value operation:
8 - x = 3
x = 8 - 3 = 5

CASE 2: 8 - x < 0, and we have to flip the sign to remove the absolute value operation:
x - 8 = 3
x = 3 + 8 = 11

Each of these answers fulfills the case restriction, and satisfies the original problem.

x = 5 OR x = 11

Hope this helps.