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 a over c equals b over c.

Assume a over c does not equal b over c. 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, ac over c does not equal bc over c. Through division, the c's cancel and ______. This contradicts the given information so a over c equals b over c.

Which statement accurately completes the proof?

Question

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 a over c equals b over c.

Assume a over c does not equal b over c. 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, ac over c does not equal bc over c. Through division, the c's cancel and ______. This contradicts the given information so a over c equals b over c.

Which statement accurately completes the proof?

anonymous · Answer

a over c equals b over c 

 a c over c does not equal b c over c 

 a = b 

 a ≠ b

zzr0ck3r · Answer

ac/c $\ne$ bc/c
and this relation will hold after cancellation, so $a\ne b$. Contradicting $a=b$.

anonymous · Answer

Thank you!

anonymous · Answer

It was wrong:(

zzr0ck3r · Answer

its what you wrote

ac/c != bc/c implies a!=b

zzr0ck3r · Answer

what did it say the answer was?

anonymous · Answer

I'm SO SORRY! You had it right! It was a ≠ b. When I clicked the down arrow on my test it changed it. Thanks for the help!

zzr0ck3r · Answer

np