Solve for x if l 2x-3 l = l x-2 l

Given the equation of absolute
values:

l 2x-3 l = l x-2 l

We
need to find the values of x that verifies the equation.

We
have 4 cases:

case(1):

2x-3 =
x-2

==> x = 1
.......(1)

case(2) :

-(2x-3) =
x-2

-2x +3 = x-2

==>
-3x = -5

==> x= 5/3
.............(2)

Case(2):

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

-2x+3 = -x
+2

==> -x =
-1

==> x=
1...............(3)

Case(4)
:

2x-3 = -(x-2)

2x-3 = -x +
2

==> 3x = 5

==>
x= 5/3.............(4)

From the above cases we conclude
that the solution is:

x= { 5/3 ,
1}