Question

The following is an indirect proof of the Multiplication Property of Equality: For real numbers a, b, and c, if a = b, then ac = bc.

Assume ac ≠ bc. According to the given information, _____. By the Division Property of Equality, one can divide the same number from both sides of an equation without changing the equation. Therefore, ac over c does not equal bc over c. Through division, the c's cancel and a ≠ b. This contradicts the given information so ac = bc.

Which statement accurately completes the proof?

ac = bc

ac ≠ bc

a = b

a ≠ b