Question

On a recent exam, a student was asked to simplify the expression:

14(6x − 3y) − 2(10y + 8x)

Their work is shown below:
Step 1: 14(6x − 3y) − 2(10y + 8x)
Step 2: 84x − 42y − 20y − 16x
Step 3: 84x − 16x − 42y − 20y
Step 4: (84x + 16x) + (−42y − 20y)
Step 5: 100x − 62y

Part A: In which step did they make a mistake, and what was it?

Part B: How would you correct the mistake and solve the problem? Show all of your work.

Answer 1

Answer:

A)  Step 4.

B)  68x - 62y

Step-by-step explanation:

Part A

The step in which the student made the mistake was in Step 4.

When combining the terms in x, the student mistakenly added 16x to 84x when they should have subtracted 16x from 84x.

Part B

Correct solution:

$\begin{aligned}& \textsf{Step 1}: \quad 14(6x-3y)-2(10y+8x)\\& \textsf{Step 2}: \quad 84x-42y-20y-16x\\& \textsf{Step 3}: \quad 84x-16x-42y-20y\\& \textsf{Step 4}: \quad (84x-16x)+(-42y-20y)\\& \textsf{Step 5}: \quad 68x-62y\end{aligned}$

In Step 4, ensure that 16x is subtracted from 84x.

Therefore, the final solution is:  68x - 62y.

Answer 2

Step-by-step explanation:

A

step 4 : -16x suddenly turned without reason into +16x.

B

correct step 4 : (84x - 16x) + (-42y - 20y)

correct step 5 : 68x - 62y