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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**