A student expanded the expression −6(4x−2/13)

Question

. Is the student's work correct? If not, what was their mistake?
-6(4x-2/13)
-6(4x)+6(- 2/13)
-24x- 12/13
(1 point)
Responses

No, the student should have multiplied 4x
and −213
by 6
.
No, the student should have multiplied 4 x and negative 2 over 13 by 6.

Yes, the student's work is correct.
Yes, the student's work is correct.

No, the student should have added −6
to 4x
and −213
.
No, the student should have added negative 6 to 4 x and negative 2 over 13.

No, the student should have multiplied 4x
and −213
by −6
.

Answer 1

The student's work is not correct. The mistake lies in how they applied the multiplication.

The original expression is:
\(-6(4x - \frac{2}{13})\).

The correct way to distribute \(-6\) across both terms inside the parentheses would be:

\(-6(4x) + -6(-\frac{2}{13})\),

which simplifies to:

\(-24x + \frac{12}{13}\).

The student incorrectly wrote \(+ 6(-\frac{2}{13})\) instead of \(-6(-\frac{2}{13})\), leading to an incorrect sign for the second term.

Thus, the correct response is:
No, the student should have multiplied \(4x\) and \(-\frac{2}{13}\) by \(-6\).