What is x if the identity is true |2-3x|-|2x-3|=0 ?

We'll solve the equation considering 4 cases of
study.

The expressions 2x-3 and 2-3x can be either positive
or negative.

Case 1:

2x-3 =
2-3x

Case 2:

-(2x-3) =
2-3x

Case 3:

2x-3 =
-(2-3x)

Case 4:

-(2x-3) =
-(2-3x)

The Case 2 and Case 3 will have the same solution.
Also Case 1 and Case 4 will have the same solution. So, we'll solve just Case 1 and Case
2:

Case 1:

2x-3 =
2-3x

We'll isolate x to the left
side:

2x + 3x = 3+2

5x =
5

We'll divide by
5:

x =
1

Case
2:

-(2x-3) = 2-3x

We'll remove
the brackets:

-2x +3 =
2-3x

We'll isolate x to the left
side:

-2x + 3x =
2-3

x =
-1

The solutions of the
equation are: {-1 ; 1}.