Solve for x the module equation |2x+16|=24?

We recall the property of absolute
value:

|x| = a>0

We'll
have to discuss 2 cases:

1) 2x+16 = 24, if 2x+16>=0
=> x belongs to [8;+infinite)

We'll subtract 16 both
sides:

2x = 24-16

2x =
8

We'll divide by 2:

x =
4

2) 2x+16 = -24, if 2x+16<0 => x belongs to
(-infinite,8)

We'll subtract 16 both sides, to isolate x to
the left side:

2x = -16 -
24

2x = -40

We'll divide by
2:

x = -20

Since
both values are in the admissible
intervals, they both become the
solutions of the equation:
{-20 ; 4}.