Answer:
 A. 1/2x-2=2x-1/2
Explanation:
The other equations are all some form of ...
 0 = <something not zero>
which has no solutions.
_____
Subtract the left side in each case:
  A: 0 = 3/2x +3/2 . . . x = -1
 B: 0 = 4 . . . . . . . . . . . no solution
 C: 0 = 3/2 . . . . . . . . . no solution
 D: 0 = 5/2 . . . . . . . . . no solution