Question

The work of a student to solve the equation 2(4x − 4) = 8 + 4x + 4 is shown below: Step 1. 2(4x − 4) = 8 + 4x + 4 Step 2. 6x − 6 = 12 + 4x Step 3. 6x − 4x = 12 + 6 Step 4. 2x = 18 Step 5. x = 9 In which step did the student first make an error and what is the correct step? Step 2, 8x − 6 = 2(6 + 2x + 2) Step 2, 8x − 8 = 12 + 4x Step 3, 6x − 4x = 12 − 6 Step 3, 6x + 4x = 12 + 6

Answer 1

Answer is step 2, 8x - 8= 12 + 4x

The student did not distribute the 2 into the parentheses properly which ruined their entire problem. With 2(4x-4) , you must multiply everything in parentheses by 2.

so 2 x 4x = 8x

2 x -4 = -8

making it 8x- 8 = 12 + 4x ( on the right side all you did was combine like terms)