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?

To determine if the student is correct, let's first analyze the equation they provided and their steps:

The original equation stated is: \[ -3(4 - 2) + 2 = +2 \]

Calculating the left side: \[ -3(2) + 2 = -6 + 2 = -4 \]

This means the left side equals \(-4\), not \(+2\). Therefore, the original equation they tried to solve is incorrect as stated. The equation should presumably say something like \(-3(4 - 2) + 2 \neq +2\).

Now, looking at the steps provided by the student:

1. Step 1: \(-12 + 3x + 2 = x + 2\)
2. Step 2: \(-10 - 3x = x + 2\)
3. Step 3: \(-8 - 3x = x\)
4. Step 4: \(-8 = 4x\) Final Answer: \(2 = -2\) or {-2}

There is an inconsistency and error right from the start as the equation setup is not correctly presented.

Error Analysis

• In Step 1, the equation appears to be formulated without a correct basis.
• The progressions and manipulations thereafter do not correspond to any correctly derived equation based on the understood context from the statement of the problem given.

The friend of the student should tell them:

• The student is incorrect.

The error appears in the very beginning with the misunderstanding of the original equation they intended to solve. The equation needs to be clarified or rephrased correctly to make sense before steps can be further analyzed or verified.