Question

Consider the sequence of steps to solve the equation: 2(x − 4) + 5x = 9x − 10 Given ⇒ 2(x − 4) + 6x = 9x − 10 Step 1 ⇒ 2x − 8 + 6x = 9x − 10 Step 2 ⇒ 2x + 6x − 8 = 9x − 10 Step 3 ⇒ 8x − 8 = 9x − 10 Step 4 ⇒ 8x − 8x − 8 = 9x − 8x − 10 Step 5 ⇒ 0 − 8 = x − 10 Step 6 ⇒ −8 = x − 10 Step 7 ⇒ −8 + 10 = x − 10 + 10 Step 8 ⇒ 2 = x + 0 Step 9 ⇒ 2 = x Which step in solving this equation is justified by the Additive Identity Property?

Answer 1

2(x − 4) + 5x = 9x − 10
Given ⇒ 2(x − 4) + 6x = 9x − 10
Step 1 ⇒ 2x − 8 + 6x = 9x − 10
Step 2 ⇒ 2x + 6x − 8 = 9x − 10
Step 3 ⇒ 8x − 8 = 9x − 10
Step 4 ⇒ 8x − 8x − 8 = 9x − 8x − 10
Step 5 ⇒ 0 − 8 = x − 10
Step 6 ⇒ −8 = x − 10
Step 7 ⇒ −8 + 10 = x − 10 + 10
Step 8 ⇒ 2 = x + 0
Step 9 ⇒ 2 = x

The Additive Identity Property states that zero added to a number equals the number.
The only place where zero is added to a number is on step 8 where you see x + 0.
Step 9 shows that x + 0 = x.

Answer: Step 9

Answer 2

Answer:

D) Step 6 ⇒ −8 = x − 10

Step-by-step explanation: