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?

Question

−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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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.