solve the equations x-1/3 - 2x-3/2 = x/6 - x+1/3

Sure, let's solve the equation step by step.

The given equation is: x - 1/3 - 2x - 3/2 = x/6 - x + 1/3

Step 1: Simplify both sides of the equation. Combine like terms on each side.

On the left side, combine x and -2x to get -x. Combine -1/3 and -3/2 to get -11/6.

On the right side, combine x/6 and -x to get -5x/6.

So, the equation now is: -x - 11/6 = -5x/6 + 1/3

Step 2: Add x to both sides of the equation to get rid of -x on the left side.

This gives: -11/6 = -5x/6 + x + 1/3

Step 3: Simplify the right side of the equation.

This gives: -11/6 = x/6 + 1/3

Step 4: Subtract 1/3 from both sides of the equation to isolate x/6.

This gives: -11/6 - 1/3 = x/6

Step 5: Simplify the left side of the equation.

This gives: -13/6 = x/6

Step 6: Multiply both sides of the equation by 6 to solve for x.

This gives: x = -13

So, the solution to the equation is x = -13.