Which step is there an error and what is the error in solving -3(4-x)+2=x+2

Question

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}

Answer 1

Let's analyze the steps provided to find the error in solving the equation \(-3(4-x) + 2 = x + 2\).

Starting Equation:

\[ -3(4 - x) + 2 = x + 2 \]

Step 1:

Distributing \(-3\):

\[ -12 + 3x + 2 = x + 2 \]

Combining terms on the left side gives:

\[ -10 + 3x = x + 2 \]

Correction to Step 1:

The correct transition to the next step after combining -12 and +2 is:

\[ 3x - 10 = x + 2 \]

Step 2:

Rearranging gives:

\[ -10 + 3x = x + 2 \]

Now, move \(x\) to the left side:

\[ 3x - x = 2 + 10 \]

This results in:

\[ 2x = 12 \]

Step 3:

Now we can solve for \(x\):

\[ x = 6 \]

Summary of Errors:

1. The error in Step 1 is where the expression \(3x - 10\) should have been derived correctly, rather than jumping to an incorrect equation.
2. Steps afterward have also misled to an incorrect path, as there was a mistake in combining like terms and rearranging the equation.

Final Answer:

The correct solution to \(-3(4-x) + 2 = x + 2\) yields \(x = 6\). Hence the final answer should reflect \(x = 6\) rather than \(x = -2\).