Find the Error: A student is simplifying the expression below. Find the student’s error and correct it.

Question

-3(x+2) + 6x=-3x + 2 + 6x
=3x +2

The student forgot to distribute (?) to both terms inside the parentheses. The student only distributed it only to the (?) term. The correct answer is (?).

What are the answers inside the (?)’s?

Answer 1

The student's error is in the distribution of the -3 to both terms inside the parentheses.

1. The student distributed the -3 incorrectly:
   • They wrote \(-3(x + 2)\) as \(-3x + 2\), but they forgot to distribute to the second term (which is +2).

So, the correct distribution of \(-3(x + 2)\) should be: \(-3(x) + (-3)(2) = -3x - 6\).

Thus, the corrected expression is: \[ -3(x + 2) + 6x = -3x - 6 + 6x \]

Then, combining like terms: \[ -3x + 6x - 6 = 3x - 6 \]

So the answers inside the (?)'s are:

• The student forgot to distribute (the -3) to both terms inside the parentheses.
• The correct answer is (3x - 6).

Answer 2

The last answer is incorrect. The choices are -3x - 2, -3x + 2, or 3(x - 2)

Answer 3

Thank you for providing the options. Let's correct the explanation based on those choices.

The student started with the expression: \[ -3(x + 2) + 6x \]

The student incorrectly wrote: \[ -3(x + 2) = -3x + 2 \] Here, they made an error by not distributing -3 to both terms correctly.

The correct distribution should be: \[ -3(x + 2) = -3x - 6 \]

So the expression simplifies correctly as: \[ -3(x + 2) + 6x = -3x - 6 + 6x = 3x - 6 \]

However, since you provided options, it seems there is room to consider a specific error form.

Looking at the choices you provided, the error is:

• The student forgot to distribute -3 to both terms inside the parentheses. The student only distributed it to the second term.

The correct option based on your choices is:

• The correct answer is -3x - 6.

None of the options you provided match \( -3x - 6 \), but if I have to choose from ( -3x - 2, -3x + 2, or 3(x - 2) ), the closest might be -3x - 2 as it is the only one that has the correct sign for -3x (though it is not correct in simplification).

So to clarify:

1. The error is due to incorrectly distributing (-3) to both terms.
2. Out of the options given, the best choice reflecting a misunderstanding in simplification in line with the student's mistake is -3x - 2. However, note that this does not relate directly to the simplified version of the original expression.