The work of a student to solve the equation 3(2x − 4) = 8 + 2x + 6 is shown below:

Question

Step 1: 3(2x − 4) = 8 + 2x + 6
Step 2: 5x − 7 = 14 + 2x
Step 3: 5x − 2x = 14 + 7
Step 4: 3x = 21
Step 5: x = 7

In which step did the student first make an error and what is the correct step? (5 points)

Step 2; 6x − 12 = 14 + 2x

Step 2; 6x − 7 = 2(6 + x + 4)

Step 3; 5x − 2x = 14 − 7

Step 3; 5x + 2x = 14 + 7

Answer 1

The error is in Step 2.

The correct step should be:

Step 2: 6x - 12 = 14 + 2x

The mistake made by the student was not distributing the 3 correctly in Step 2.