Question

Callie solved this one-variable equation. When she was done, she tried to verify her answer, but found that it was wrong. Can you find her mistake?

1
2
(4k + 8) = 10

1. 2k + 16 = 10

2. 2k = −6

3. k = −3

What was Callie’s mistake?
Callie should have added 10 to both sides in step 2.
In step 1, when Callie distributed the One-half to the 8, she multiplied incorrectly.
Callie divided by 2 instead of multiplying by 2 in step 3.
Callie should have added 16 to both sides in step 2.

Answer 1

The equation is (1/2)(4k + 8) = 10. Callie’s Step 1 is wrong: (1/2)(4k + 8) = 2k + 4, not 2k + 16. She incorrectly computed (1/2)·8 = 16. The correct work:

(1/2)(4k + 8) = 10
2k + 4 = 10
2k = 6
k = 3

So the correct mistake is: "In step 1, when Callie distributed the One-half to the 8, she multiplied incorrectly."