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

Question

-6 (4x - 12/13)
-6 (4x) + 6 (-2/13)
-24x - 12/13
(1 point)
No, the student should have multiplied -6 to 4x and -2/13
No, the student should have multiplied 4x and -2/13 by 6.
No, the student should have added 4x and -2/13 by -6
Yes, the student's work is correct.

Answer 1

Let's analyze the expression step by step.

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

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

1. Multiply \(-6\) by \(4x\): \[-6 \times 4x = -24x\]

2. Multiply \(-6\) by \(-\frac{2}{13}\): \[-6 \times -\frac{2}{13} = \frac{12}{13}\] (since multiplying two negatives gives a positive).

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

Now, let's compare this with the student's work:

• The student wrote \(-6(4x - 12/13)\) which is incorrect because they altered the coefficient of \(-2/13\) to \(-12/13\).
• The next line, \(-6(4x) + 6(-\frac{2}{13})\), is incorrect because the multiplication of \(-6\) and \(-\frac{2}{13}\) should yield \(\frac{12}{13}\), not \(-\frac{12}{13}\).
• Thus, their final result of \(-24x - \frac{12}{13}\) is also incorrect.

Therefore, the student's work is incorrect. The correct answer would be:

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