To solve this equation, we can start by simplifying both sides of the equation.

First, distribute the 2 and the -3:

2(x - 1/3) - 3(x - 1/2) = 1/2x

2x - 2/3 - 3x + 3/2 = 1/2x

Next, combine like terms:

(2x - 3x) + (-2/3 + 3/2) = 1/2x

-x + (4/6 - 9/6) = 1/2x

-x - 5/6 = 1/2x

Now, let's get rid of the fractions by multiplying both sides of the equation by the least common denominator, which is 6:

6(-x - 5/6) = 6(1/2x)

-6x - 5 = 3x

Next, let's isolate the x terms on one side of the equation:

-6x - 3x = 5

-9x = 5

Finally, divide both sides of the equation by -9 to solve for x:

x = -5/9

Therefore, the solution to the equation is x = -5/9.