Question

A student solved the equation below. They asked a friend to check their solution and work. What should their friend tell them? Are they correct? If they are not correct, in which step did the student make an error?

−3(4−x)+2=x+2


Step 1: −12+3x+2=x+2


Step 2: −10−3x=x+2


Step 3: −8−3x=x


Step 4: −8=4x



Final Answer: x=−2
or {−2}


(1 point)
Responses

The student is correct
The student is correct - no response given

The student is incorrect
The student is incorrect - correct
Question 2
If the student is incorrect, explain in which step the student made an error AND what the error was?(2 points)
0 / 10000 Word Limit
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page 5 of 5

Answer 1

The student's solution is incorrect. Let's review each step to identify the error:

1. **Original Equation**:
\[
-3(4−x)+2=x+2
\]

2. **Step 1**:
\[
-12 + 3x + 2 = x + 2
\]
This step is correct. The left side simplifies to \(-12 + 3x + 2 = 3x - 10\).

3. **Step 2**:
\[
-10 - 3x = x + 2
\]
This step is incorrect. The correct simplification from Step 1 should yield:
\[
3x - 10 = x + 2
\]

4. **Step 3**:
\[
-8 - 3x = x
\]
This step relies on the incorrect Step 2. Therefore, this step is also incorrect.

5. **Step 4**:
\[
-8 = 4x
\]
This step also derives from incorrect prior steps and is therefore invalid.

6. **Final Answer**:
\[
x = -2
\]
Since the steps leading to this solution are incorrect, the final answer is also incorrect.

### Summary of the Error:
The student made an error in **Step 2** where they incorrectly rearranged the terms and did not properly simplify the equation from Step 1. The correct equation should have been:
\[
3x - 10 = x + 2
\]
This led to an incorrect solution in subsequent steps.

### Correct Steps from Step 1:
Starting from:
\[
3x - 10 = x + 2
\]

You would then move \(x\) to the left side:
\[
3x - x = 2 + 10
\]
which simplifies to:
\[
2x = 12
\]
Thus,
\[
x = 6.
\]

As a result, the student's friend should tell them they are incorrect, and the error is in Step 2.