The following is an indirect proof of the division property of equality: for real numbers, a, b, and c, if a = b and c ≠ 0, then . assume . according to the given information, a = b. by the multiplication property of equality, one can multiply the same number to both sides of an equation without changing the equation. therefore, . through division, the c's cancel and this contradicts the given information so . which statement accurately completes the proof? a = b a ≠ b

The statement above establishes the following:

If:
(1)
(2) 

Then we must assume that in fact , therefore if we multiply the same number, say c, to both sides of an equation this one is not affected, then we have:

(3) 

First answer.

Through division, the c's cancel and zero. Let's prove it:

a. If we divide (3) by c, this is canceled and the equation (3) is converted to:

All right up here

b. If we divide (3) by (a - b), this term is canceled and the equation (3) is converted to:

But this is a contradiction given that in the statement above  

Second answer. Which statement accurately completes the proof?

The statement that completes the proof is necessarily: 



For example:





Given that:
and

Then:

 

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