To solve this equation, we need to simplify both sides and then isolate the variable x.

Starting with the left side of the equation:
x - 2/3 + 1

Combine the -2/3 and +1 terms by finding a common denominator:
x - 2/3 + 3/3
x + 1/3

Now, the equation becomes:
x + 1/3 = x - 1/2

To isolate the variable x, we need to get all terms with x on one side of the equation:
x - x = -1/2 - 1/3
0 = -5/6

Since we get the statement 0 = -5/6, it means that there is no solution to this equation.