A student expanded an expression, as shown. Is the student's work correct? If not, what was their mistake?

Question

−6 ( 4x − 2/ 13 )
−6(4x) + 6 ( − 2/13)
−24x − 12/13

A. Yes, the student's work is correct.
B. No, the stuent should have multiplied 4x and -2/13 by -6.
C. No, the student should have added -6 to 4x and -2/13.
D. No, the student should have multiplied 4x and -2/13 by 6.

Answer 1

The student's work is not correct. Let's analyze the steps they took:

1. They correctly wrote the expression as \(-6(4x - \frac{2}{13})\).
2. The student then wrote \(-6(4x) + 6(-\frac{2}{13})\).

Here is where the mistake happens. When you distribute \(-6\) to both \(4x\) and \(-\frac{2}{13}\), you should multiply by \(-6\) in both cases:

\[ -6(4x) \text{ which gives } -24x \] \[ -6\left(-\frac{2}{13}\right) \text{ which gives } \frac{12}{13} \]

Thus, the correct distributed expression should have been: \[ -24x + \frac{12}{13} \]

The student mistakenly wrote \(6(-\frac{2}{13})\) as \(-\frac{12}{13}\) (instead of \(+\frac{12}{13}\)).

Therefore, the correct answer is:

B. No, the student should have multiplied 4x and -2/13 by -6.