Clearly show and explain each step for full credit.

solve the inequality |4x-3|=5

|4x-3|=5

4x-3 = 5 OR 4x-3 = -5
4x = 8 or 4x = -2
x = 2 or x = -1/2

Note:
really I should have started with
4x-3 = 5 OR -4x+3 = 5
but with absolute value "equations" you may begin the way I did,
BUT, if you had an inequation, you MUST do it this last way
e.g. |4x-3| < 5
4x-3 < 5 AND -4x +3 < 5
4x < 8 AND -4x < 2
x < 2 AND x > -1/2