Question

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) ________________________
y + x + (–x) = y + [x + (–x)] Associative Property of Addition
y + [x + (–x)] = y + 0 Additive Inverse Property
y + 0 = y Additive Identity Property

A.
Definition of Subtraction

B.
Additive Inverse Property

C.
Additive Identity Property

D.
Opposite of a Sum Property

Answer 1

What's the question?

Answer 2

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) ________________________
y + x + (–x) = y + [x + (–x)] Associative Property of Addition
y + [x + (–x)] = y + 0 Additive Inverse Property
y + 0 = y Additive Identity Property

Answer 3

A.
Definition of Subtraction

B.
Additive Inverse Property

C.
Additive Identity Property

D.
Opposite of a Sum Property

Answer 4

D

Answer 5

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