Question

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

Assume____________. According to the given information, a = b. By the Subtraction Property of Equality, one can subtract the same number from both sides of an equation without changing the equation. Therefore, a + c − c ≠ b + c − c. Through subtraction, the c's cancel and a ≠ b. This contradicts the given information so a + c = b + c.

Which statement accurately completes the proof?

a + c = b + c

a + c ≠ b + c

a ≠ b

b = c