Lets see your work. How did you get x>1/2 , from 3/2x-3/4>0 ?
A large part of your problem is that what you give as the question itself is ambiguous- use parentheses!
If the problem was (5/6)x+(2/3)x>3/4, then x> 1/2 is exactly right. However, it appears that your problem is really 5/(6x)+ 2/(3x)> 3/4. If that is what the inequality is, then, as SammyS said, you arrive at 1/x> 1/2 so that 0< x< 2. (If 1/x> 1/2 then x must be positive.)