Solve the absolute value equation: ||2x+1|-18|=4

The easiest way to solve any absolute value problem is to determine all possible equations with respect to the signs of the expressions. This equation has 4 possibilities: 


case 1)
2x+1-18=4 
2x=21
x=21/2 

case 2)
-2x-1-18=4
-2x=23
x=-23/2 


case 3)
2x+1-18=-4
2x=13
x=13/2 

case 4)
-2x-1 -18=-4
-2x=15
x=-15/2