Solve for the variable x in terms of y and z, assuming $y \neq \frac{1}{2}$: \[xy + x = \frac{3x + 2y + z}{2}.\]
xy + x = (3x + 2y + z) / 2
2 (xy + x) = 3x + 2y + z
2xy + 2x = 3x + 2y + z
2xy - x = 2y + z
x ( 2y -1) = 2y + z
x = ( 2y + z) / ( 2y -1)
+52 
