Question

Consider the sequence of steps to solve the equation: 2(x − 4) + 6x = 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 Distributive Property?
A Step 1 ⇒ 2x − 8 + 6x = 9x − 10Step 1 ⇒ 2x − 8 + 6x = 9x − 10
B Step 2 ⇒ 2x + 6x − 8 = 9x − 10Step 2 ⇒ 2x + 6x − 8 = 9x − 10
C Step 3 ⇒ 8x − 8 = 9x − 10Step 3 ⇒ 8x − 8 = 9x − 10
D Step 4 ⇒ 8x − 8x − 8 = 9x − 8x − 10Step 4 ⇒ 8x − 8x − 8 = 9x − 8x − 10

Answer 1

A Step 1 ⇒ 2x − 8 + 6x = 9x − 10

The Distributive Property is applied in Step 1 when distributing the 2 to both terms inside the parentheses. This can be seen by expanding 2(x - 4).