Question

Find the Error A student is simplifying the expression below. Find the student's error and correct it. -3(x+2)+6x=-3x+2+6x
=3x+2
The student forgot to distribute (choices: 2, -3.) to both terms inside the parentheses. The student only distributed it only to the (choices: first, second.) term. The correct answer is (choices: -3x-2, -3x+2, 3(x-2).)

Answer 1

no thats not the correct answer

Answer 2

Let's analyze the expression step by step:

The original expression is:
\[ -3(x + 2) + 6x \]

The correct way to distribute \(-3\) to both terms inside the parentheses is:
\[ -3(x) + -3(2) + 6x = -3x - 6 + 6x \]

Now, combine like terms:
\[ -3x + 6x - 6 = (6x - 3x) - 6 = 3x - 6 \]

Now, comparing this with what the student did, the student's mistake was:
- The student distributed \(-3\) incorrectly, only distributing it to the second term instead of both terms. They wrote:
\[ -3(x + 2) = -3x + 2 \] (which is incorrect).

The corrected distribution gives:
\[ -3x - 6 + 6x \]

Thus, the student's error was in distributing \(-3\) to both terms inside the parentheses, and the student only distributed it to the second term.

The correct answer to the expression is:
\[ 3x - 6 \]

So filling in the blanks:
The student forgot to distribute \(-3\) to both terms inside the parentheses. The student only distributed it to the second term. The correct answer is \(3x - 6\).

Answer 3

Apologies for any confusion. Let's carefully re-evaluate the steps in the expression to correctly identify the student's error and provide the right solution.

Given the expression:
\[
-3(x + 2) + 6x
\]

1. **Distributing**:
The student should distribute \(-3\) to both terms inside the parentheses:
\[
-3(x) - 3(2) + 6x = -3x - 6 + 6x
\]

2. **Combining like terms**:
Now, combine \(-3x\) and \(6x\):
\[
-3x + 6x - 6 = 3x - 6
\]

Now let's look at the student's work:
- The student's expression was:
\[
-3x + 2 + 6x
\]
which should have been \(-3x - 6 + 6x\).

In the student's work, they mistakenly wrote \( -3x + 2 \) instead of \( -3x - 6 \). This means you identified a sign error in their distribution.

Thus, the breakdown of the student's error is as follows:
- The student forgot to distribute \(-3\) to both terms inside the parentheses.
- The student only distributed it to the second term.
- The correct answer should be \(3x - 6\).

With these points clarified, can you confirm what the choices are for the correction? Thank you for your patience!