Question

A student expanded the expression −6(4x−2 over 13)
. Is the student's work correct? If not, what was their mistake?



(1 point)
Responses

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

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 negative 6.

Yes, the student's work is correct.

Answer 1

Let's analyze the expression you provided: \(-6(4x - \frac{2}{13})\).

To expand this expression, we need to distribute \(-6\) to both terms inside the parentheses:

1. First, distribute \(-6\) to \(4x\):
\[
-6 \times 4x = -24x
\]

2. Next, distribute \(-6\) to \(-\frac{2}{13}\):
\[
-6 \times -\frac{2}{13} = \frac{12}{13}
\]

Putting it all together, the expanded expression is:
\[
-24x + \frac{12}{13}
\]

Now, let's evaluate the student's work against the correct procedure:

- The correct operation is to multiply \(4x\) and \(-\frac{2}{13}\) by \(-6\), yielding \(-24x\) and \(\frac{12}{13}\), respectively.

Looking at the provided responses:

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

This response correctly identifies that the student should have multiplied each term inside the parentheses by \(-6\).

Therefore, the correct option is: **No, the student should have multiplied 4x and −2 over 13 by −6.**