Question

A student attempts to solve for c in the equation below.

Which statement best applies to the work shown below?

A.
The student followed all rules correctly and solved for c.
B.
In step 2 of the student’s work they made a mathematical error.
C.
The student’s answer is negative but it should be positive.
D.
The student combined like terms incorrectly in step 1.

Answer 1

A. The student followed all rules correctly and solved for c

Explanation:

Given the equation
`3c + 6 - 4c = 12 c + 7`, the student followed all rules correctly because:

• step 1: He combined like terms correctly for c in the left side from the equation

`3c - 4c = - c`

• step 2: he subtracted 6 from both sides

`-c +6 + (-6) = 12c +7+(-6)`

• step 3: To isolate “c”, he substracted 12c from both sides

`-c +(-12c) = 12c +(-12c) +1`

• Step 4: finally he divided both sides by
  `-13`

`-(13c)/(13)= -(1)/(13)`

And he got it:

`c = -(1)/(13)`

Now we´ll check this work with the original equation:

`3c + 6 - 4c = 12 c + 7`

`3(-(1)/(13)) + 6 - 4(-(1)/(13)) = 12(-(1)/(13)) + 7`

`-(3)/(13) + 6 +(4)/(13) = -(12)/(13) +7`

`6 + (1)/(13) = (79)/(13)`

`(79)/(13) = (79)/(13)`

Very good √

Answer 2

I think the correct answer from the choices listed above is option A. From the image given above, the steps made by the students were all correct and she was able to solve for the value of c. Hope this answers the question. Have a nice day.