Let's first simplify the equation:

1/3(6x - 1) - (0.5 - x/2) = 0

Distribute the 1/3 and distribute the negative sign before the parenthesis:

2x - 1/3 - 0.5 + x/2 = 0

Combine like terms:

2x + x/2 - 1/3 - 0.5 = 0

To combine x and x/2, we first get a common denominator:

2x + x/2 = 4x/2 + x/2 = (4x + x)/2 = 5x/2

Now we can rewrite the equation:

5x/2 - 1/3 - 0.5 = 0

To get rid of the fractions, let's multiply the entire equation by 6 to clear the denominators:

6(5x/2) - 6(1/3) - 6(0.5) = 60

15x - 2 - 3 = 0

15x - 5 = 0

15x = 5

x = 5/15

x = 1/3

Therefore, the solution to the equation is x = 1/3.