Question

Which reason for step 4 completes the proof?

Prove: -(a + b) + a = -b

Answer 1

Identity Property of Addition.

Answer 2

Reason which completes the proof of step 4 is:

Identity property of addition

Explanation:

-(a+b)+a= -b

= -a+ (-b)+a (distributive property)

= -a+a+(-b) (Commutative property of Addition)

= 0+ (-b) (Additive inverse property)

= -b (Identity property of addition)

(Identity property of addition says that if 0 is the identity element and a is any element

Then, a+0=0+a=a)

So, reason which completes the proof of step 4 is:

Identity property of addition