To solve the equation 3x - 1/3 = 2 - x/2, we can follow these steps:

1. Multiply both sides of the equation by the least common multiple (LCM) of the denominators to eliminate the fractions. In this case, the LCM of 3 and 2 is 6, so we can multiply both sides by 6:

     6(3x - 1/3) = 6(2 - x/2)

2. Simplify both sides by distributing the multiplication:

     18x - 2 = 12 - 3x

3. Add 3x to both sides to get all the x terms on one side of the equation:

     18x + 3x - 2 = 12

4. Combine like terms:

     21x - 2 = 12

5. Add 2 to both sides to isolate the variable term:

     21x = 14

6. Divide both sides by 21 to solve for x:

     x = 14/21 = 2/3

Therefore, the solution to the equation 3x - 1/3 = 2 - x/2 is x = 2/3.

<=> 2(3x-1)=3(2-x)
<=> 6x-2=6-3x
<=> 6x+3x=6+2
<=> 9x=8
<=> x=8/9