Question

please explain?



What is the missing reason in the proof?

Prove –(–y – x) – x = y
Statements Reasons
–(–y – x) – x = –[–y +(–x)] – x Definition of subtraction
–[–y +(–x)] – x = y + x – x Opposite of a sum property
y + x – x = y + x + (–x) Definition of subtraction
y + x + (–x) = y + [x + (–x)] Associative Property of Addition
y + [x + (–x)] = y + 0 Additive Inverse Property
y + 0 = y ________________________


A.
Symmetric Property

B.
Additive Inverse Property

C.
Additive Identity Property

D.
Opposite of a Sum Property

Answer 1

Hint: \(x*1 = x\) is an identity.

Answer 2

umm i am not sure D?

Answer 3

For the 4 answer choices, can you explain them? If you know what each of those properties do, then you should be able to answer this yourself. and we can confirm the answer and guide you if you get stuck.

Answer 4

You are guessing D: Opposite of a Sum property

in the equation \[y +0 = y\]I see a sum, but I don't see an opposite. What makes you think that would be a good guess?

Answer 5

Earlier in the proof, they do use the opposite of a sum property:
\(–[–y +(–x)] – x = y + x – x\) Opposite of a sum property
but that doesn't look anything like what we have in the mystery line

and now someone has given away the answer...

Answer 6

Remember. ....Zero is additive identity
And 1 is multiplicative identity.

Answer 7

C

Answer 8

Yes

Answer 9

Yes, the additive identity property is why \[y+0 = y\]is a justifiable step in the proof.

Answer 10

thanks m80

Answer 11

It would be very good if you could look at all of those reasons and understand what they mean...

Answer 12

i do know

Answer 13

could you give me an example of the symmetric property?