Question

Two students solved the same multi-step equation. Which student is correct? Explain the error. Student A Student B 2x - 4(3x + 6) = -6(2x + 1) - 4 2x - 4(3x + 6) = -6(2x + 1) - 4 2x - 12x + 6 = -12x + 1 - 4 2x - 12x - 24 = -12x - 6 - 4 -10x + 6 = -12x - 3 -10x - 24 = -12x - 10 2x = -9 2x = 14 x = -4 _1 2 x = 7

Answer 1

Student B is correct

Student A failed to distribute -4 and -6 when opening the brackets in the first step

Explanation:

The solution Student A gave was:

2x - 4(3x + 6) = -6(2x + 1) - 4

2x - 12x + 6 = -12x + 1 - 4

-10x + 6 = -12x - 3

2x = -9

x = -4 _1 2 ( -4 1/2)

The solution Student B gave was:

2x - 4(3x + 6) = -6(2x + 1) - 4

2x - 12x - 24 = -12x - 6 - 4

-10x - 24 = -12x - 10

2x = 14

x = 7

Student B is correct.

Explanation of the error:

Student A failed to distribute -4 and -6 when opening the brackets in the first step.

That is,

2x - 4(3x + 6) = -6(2x + 1) - 4

To open this bracket, we will distribute, -4 and -6 so that we get

2x (-4 × 3x) + (-4 × +6) = (-6×2x) + (-6 × +1) - 4

Then we will get

2x -12x -24 = -12x -6 -4

Adding the like terms

-10x - 24 = -12x - 10

Collecting like terms

-10x + 12x = -10 + 24

∴ 2x = 14

x = 14 / 2

Hence,

x = 7