By definition of absolute value,
• if x + 4 ≥ 0, then |x + 4| = x + 4, and so
|x + 4| = 3x - 5
x + 4 = 3x - 5
2x = 9
x = 9/2
• otherwise, if x + 4 < 0, then |x + 4| = -(x + 4), so that
|x + 4| = 3x - 5
-(x + 4) = 3x - 5
-x - 4 = 3x - 5
4x = 1
x = 1/4
However, in the second case we assume x + 4 < 0, or x < -4. So x = 1/4 is an extraneous solution, and the only solution would be x = 9/2.