|2x -3|-3 = 4   is equivalent to

|2x-3| = 4 + 3 = 7   is equivalent to

|x-1.5| = 3.5.


The solutions are those "x" that are remoted in 3.5 units from 1.5, i.e. these two values

x = 1.5 - 3.5 = -2   and   x = 1.5 + 3.5 = 5.


Answer. The two solutions are x= -2  and  x= 5.