Question

What is the missing reason in the proof?

Prove –(–y – x) – x = y

–(–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
(blank)

Answer options for (blank):

A. Symmetric Property

B. Additive Inverse Property

C. Additive Identity Property

D. Opposite of a Sum Property

Answer 1

Option C is correct.

Explanation:

The last step is y+0 =y

This represents additive identity property.

This property states if zero is added to any number we get the same number.i.e if 0 is added to y then we get y (y+0=y)

So, Option C is correct