l x-3 l = l 2x+5 l find x values

We are given l x-3 l = l 2x+5
l.

Now l x-3 l is equal to (x-3) if (x-3) is greater than
or equal to 0 and is equal to -(x-3) if (x-3) is less than
0.

Similarly l 2x+5 l is equal to (2x+5) if (2x+5) is
positive or is equal to -(2x+5) if (2x+5) is negative.

Now
if x-3 < 0

=> x <
3

=> 2x + 5 can be positive or
negative.

Therefore -( x-3 ) = 2x +
5

=> 3 - x = 2x +
5

=> 3x = -2

=>
x = -2/3

or -(x - 3) = -2x -
5

=> 3-x = -2x -
5

=> x = -8

Now if x -3
> 0

=> x >
3

=> 2x +5 >
0

Therefore (x-3) =
(2x+5)

=> x =
-8

Therefore the possible values of x are
-2/3 and -8