To solve the equation 2(1/2 - x) - 3(x - 1/3) = 7/2, we can start by simplifying both sides of the equation.

First, distribute the 2 to both terms inside the parentheses:
2(1/2 - x) = 1 - 2x

Next, distribute the -3 to both terms inside the parentheses:
-3(x - 1/3) = -3x + 1

Now, the equation becomes:
1 - 2x - 3x + 1 = 7/2

Combine like terms:
-5x + 2 = 7/2

To get rid of the fraction, we can multiply both sides of the equation by 2:
2(-5x + 2) = 2(7/2)
-10x + 4 = 7

Next, subtract 4 from both sides of the equation:
-10x + 4 - 4 = 7 - 4
-10x = 3

Finally, divide both sides of the equation by -10 to solve for x:
-10x/-10 = 3/-10
x = -3/10

Therefore, the solution to the equation 2(1/2 - x) - 3(x - 1/3) = 7/2 is x = -3/10.