Solve an absolute inequality

|2x - 5/3| > 1 ???

This is what im getting but dont know if its correct?
.....set up 2 equations ..one positive..one negitive


|2x - 5/3| > 1 ............. |2x - 5/3| < -1

multiply both sides by 3 to remove fraction
3(2x - 5/3) > 1(3) ............ 3(2x - 5/3) <-1(3)

2x-5 > 3............. 2x - 5 <-3

2x>3+5.............. 2x< -3 +5

2x >8 ................. 2x< 2

x>4 .................... x<1

When to sub in 4 and 1 to the initial equations it dosent seem to make sense?
Please tell me where i am going wrong?

Your mistake was in multiplying the bracket by 3.

3(2x - 5/3) = 6x - 5

The rest of the working was OK so you get

6x > 8 or 6x < 2 ----> x > 4/3 or x < 1/3

Edit. By the way, your second line is not technically correct although I see what you mean and it doesn't make the working wrong.

I2x - 5/3I > 1 ----> 2x - 5/3 > 1 or 2x - 5/3 < -1

The point is that I2x - 5/3I < -1 is wrong because absolute value is not negative.