Question

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

Step 1. 4(3x − 4) = 8 + 4x + 8
Step 2. 7x − 8 = 16 + 4x
Step 3. 7x − 4x = 16 + 8
Step 4. 3x = 24
Step 5. x = 8

In which step did the student first make an error and what is the correct step?

A. Step 2, 12x − 16 = 16 + 4x
B. Step 2, 12x − 8 = 2(4 + 2x + 4)
C. Step 3, 7x − 4x = 16 − 8
D. Step 3, 7x + 4x = 16 + 8

Answer 1

4(2x − 4) = 8 + 2x + 8
Distribute 4:
8x - 8 = 8 + 2x + 8 ← Error here, she wrote as 6x - 8 = 8 + 2x + 8
8x - 8 = 2x + 16
8x - 2x = 16 + 8
6x = 24
x = 6
Answer: Step 2; 8x − 16 = 16 + 2x

Answer 2

The answer is A. Step 2, 12x-16=16+4x.
This is because you have to distribute the numbers in the parenthesis by multiplying the number bordering the outside of the left parenthesis with the numbers inside the parenthesis to make the first part of the equation complete.
So, multiplying 4(3x-4) would give you 12x-16.
What the student did wrong were his operations. He was supposed to multiply, not add. If he multiplied (distributed the equation in the parenthesis), then he would have gotten the rest of the steps differently.