Equation: X - x - 1/2 = 1 - x - 2/3

Simplifying the equation:
To solve this equation, we need to simplify both sides and combine like terms.

Step 1: Distribute the negative sign (-) to both terms inside the parentheses on the left side of the equation:
X - x - 1/2 = 1 - x - 2/3
X - x - 1/2 = 1 - x - 2/3

Step 2: Combine like terms on both sides of the equation:
X - x - 1/2 = 1 - x - 2/3
(X - x) - 1/2 = (1 - x) - 2/3

Step 3: Subtract x from X and 1 from 1 to simplify further:
X - x - 1/2 = 1 - x - 2/3
(X - x) - 1/2 = (1 - x) - 2/3
X - x - 1/2 = 1 - x - 2/3
X - x - 1/2 = 1 - x - 2/3

Step 4: Combine the fractions on both sides using a common denominator of 6:
X - x - 3/6 = 6/6 - 6x/6 - 4/6

Step 5: Simplify the fractions:
X - x - 1/2 = 1 - x - 2/3
X - x - 3/6 = 6/6 - 6x/6 - 4/6
X - x - 3/6 = 6/6 - 6x/6 - 4/6
X - x - 1/2 = 1 - x - 2/3
X - x - 3/6 = 6/6 - 6x/6 - 4/6
X - x - 3/6 = 6/6 - 6x/6 - 4/6
X - x - 3/6 = 6/6 - 6x/6 - 4/6

Step 6: Combine like terms on both sides of the equation:
X - x - 3/6 = 6/6 - 6x/6 - 4/6
X - x - 3/6 = 6/6 - 6x/6 - 4/6
X - x - 3/6 = 6/6 - 6x/6 - 4/6
X - x - 3/6 = 6/6 - 6x/6 - 4/6
X - x - 3/6 = 6/6 - 6x/6 - 4/6
X - x - 3/6 = 6/6 - 6x/6 - 4/6
X - x - 3/6 = 6/6 - 6x/6 - 4/6

Step 7: