Which expression is equivalent to 10 − (x − 3)?

Which expression is equivalent to 10 − (x − 3)?

• A. x − 13
• B. 3 − x
• C. 13 − x
• D. 10 − x

Answer: (C)

Think about distributing the minus sign across the parentheses. Subtracting x gives −x, and subtracting −3 becomes +3. So 10 − (x − 3) = 10 − x + 3. Combine the constants to get 13 − x. That matches the expression with x first and a constant after it, so 13 − x is equivalent to the original. The other forms miss the +3, or rearrange the signs in a way that doesn’t reflect the distributed subtraction (for example, 10 − x lacks the +3, and 3 − x isn’t including the 10).

Think about distributing the minus sign across the parentheses. Subtracting x gives −x, and subtracting −3 becomes +3. So 10 − (x − 3) = 10 − x + 3. Combine the constants to get 13 − x. That matches the expression with x first and a constant after it, so 13 − x is equivalent to the original.

The other forms miss the +3, or rearrange the signs in a way that doesn’t reflect the distributed subtraction (for example, 10 − x lacks the +3, and 3 − x isn’t including the 10).