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

Question

Mathematics

Kendall Petty

28 May, 21:06

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

+3

Answers (1)

Know the Answer?

Roger Orozco · Answer 1

Option C is correct.

Step-by-step 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