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 4?
A) Subtraction Property of Equality
B) Commutative Property of Addition
C) Addition Property of Equality
D) Additive Inverse Property

Answer 1

A) Subtraction Property of Equality

Explanation:

In step 4, we see that 8x has been subtracted from each side.

The property that allows us to subtract something from both sides of the equation is the subtraction property of equality.

Answer 2

A) Subtraction Property of Equality