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?

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.

Step 9