To solve this equation, we first need to combine like terms on both sides of the equation.

1/12 + 1/4 - 1/3x + 1/3 = 1/2 + 1/2x

To combine the fractions on the left side of the equation, we first find a common denominator. The least common multiple of 12, 4, and 3 is 12, so we rewrite the fractions with a denominator of 12:

1/12 + 3/12 - 4/12x + 4/12 = 6/12 + 6/12x

Now we can combine the fractions on the left side:

4/12 - 4/12x = 6/12 + 6/12x

Simplifying further:

-4/12x - 6/12x = 6/12 - 4/12

-10/12x = 2/12

Dividing by -10/12 on both sides to isolate x:

x = (2/12) / (-10/12)
x = 2/12 * -12/10
x = -24/120
x = -1/5

Therefore, the solution to the equation is x = -1/5.