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Question
Consider the sequence of steps to solve the equation: 3(x − 4) + 5x = 9x − 36

Given ⇒ 3(x − 4) + 5x = 9x − 36
Step 1 ⇒ 3x − 12 + 5x = 9x − 36
Step 2 ⇒ 3x + 5x − 12 = 9x − 36
Step 3 ⇒ 8x − 12 = 9x − 36
Step 4 ⇒ 8x − 8x − 12 = 9x − 8x − 36
Step 5 ⇒ 0 − 12 = x − 36
Step 6 ⇒ −12 = x − 36
Step 7 ⇒ −12 + 36 = x − 36 + 36
Step 8 ⇒ 24 = x + 0
Step 9 ⇒ 24 = x

Which property yields Step 7?
Responses
A Additive Inverse PropertyAdditive Inverse Property
B Additive Identity PropertyAdditive Identity Property
C Addition Property of EqualityAddition Property of Equality
D Commutative Property of Addition

Answer 1

The property that yields Step 7, where you add 36 to both sides of the equation \(-12 = x - 36\), is the Addition Property of Equality. This property states that if you add the same amount to both sides of an equation, the two sides remain equal.

So the correct response is:

C. Addition Property of Equality