To solve this equation, we first need to simplify the left side by distributing the coefficients:

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

Next, we combine like terms:

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

Now, we can combine the x terms on the left side:

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

To combine the x terms, we need a common denominator:

3/6x - 2/6x = x + 1 - 4/6

1/6x = x + 1 - 2/3

Now, we can isolate the x term by multiplying both sides by 6:

x = 6(x + 1 - 2/3)

x = 6x + 6 - 4

x = 6x + 2

Subtracting 6x from both sides gives:

x - 6x = 2

-5x = 2

Finally, divide by -5 to solve for x:

x = -2/5

Therefore, the solution to the equation is x = -2/5.