Variable, reciprocals, and fractions..

I came across another question which has just stumped me because I worked it over about 5 times and I couldn't figure out how the book got the answer. I've obtained messed up answers and none have them have been...

Answer: 6

Problem:

2x - 3(x-2)/2 = 7 - x-3/3

The thing that probably messed me up the most was the fact that I didn't know how to get the variable fractions out of the way.

I really don't remember the book covering that, therefore I sucked at it.

I did somehow try to solve it: :confused:

2(2x - 3(x-2)/2) = (7 - x-3/3)2

4x - 3x - 6 = 14 - 2x-6/3

x - 6 = 14... +6+14...

x = 20 - 2x-6/6

3(x) = (20 - 2x-6/3)3

3x = 60 - 2x - 6

+2x

8x = 54

8/8 = 54/8

= 6.75

So basically i'm screwing up somewhere and I don't know where but I'm not getting the right answer.