Question

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 2?
Responses
A Additive Inverse Property
B Additive Identity Property
C Addition Property of Equality
D Commutative Property of Addition

Answer 1

The transition from Step 1 to Step 2 involves rearranging the terms in the equation while keeping them on the same side. This change does not alter the equality of the expression. Thus, the property used here is the **Commutative Property of Addition**, which states that the order in which you add numbers does not affect the sum.

Therefore, the correct answer is:

D. Commutative Property of Addition