Question

Two more students, Christian and Esther, are solving the same equation. They take a different approach to solving the equation, but they each make an error in the first two lines of their work, shown below.

15 - 3(x - 2) + 6x = 3(13)
Christian's Work:
a) 12(x - 2) + 6x = 39
b) 12x - 24 + 6x = 39
c) 15 - 6 - 3 + 6x = 39
Esther's Work:
a) 12(x - 2) + 6x = 39
b) 15 - 32 - 6 + 6x = 39
c) 15 - 6 - 3 + 6x = 39
Explain the error that each student made.
a) Christian made an error in the second line.
b) Christian made an error in the third line.
c) Esther made an error in the second line.
d) Esther made an error in the third line.

Answer 1

Christian made an error in the second line by incorrectly distributing the 12. Esther made an error in the third line by simplifying the terms incorrectly.

Step-by-step explanation:

Christian made an error in the second line. He incorrectly distributed the 12 to both the x and the -2, resulting in a simplification error. The correct step would be 12(x - 2) = 12x - 24.

Esther made an error in the third line. She simplified 15 - 32 - 6 + 6x incorrectly, combining the terms 15 and -32 as 15 - 32 = -17, but the correct result is 15 - 32 = -17.