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 Combining Like Terms? A) Step 1 ⇒ 2x − 8 + 6x = 9x − 10 B) Step 2 ⇒ 2x + 6x − 8 = 9x − 10 C) Step 3 ⇒ 8x − 8 = 9x − 10 D) Step 4 ⇒ 8x − 8x − 8 = 9x − 8x − 10

Answer 1

Answer: Step 3 >8x-8=9x-10

Answer 2

The like terms 2x and 6x of Step 2 are combined in Step 3:

... C) Step 3 ⇒ 8x -8 = 9x -10