Question

The work of a student trying to solve the equation 3(4x – 2) = 9 + 2x + 5 is shown below:

Step 1: 3(4x – 2) = 9 + 2x + 5

Step 2: 12x – 2 = 14 + 2x

Step 3: 12x – 2x = 14 + 2

Step 4: 10x = 16

Step 5: x = 1.6

In which step did the student first make an error and what is the correct step? (4 points)


Step 2: 12x – 2 = 4 + 2x
Step 3: 12x – 2x = 14 – 2
Step 3: 12x + 2x = 14 + 2
Step 2: 12x – 6 = 14 + 2x

Answer 1

Does \[3(4x-2) = 12x-2\]?

Answer 2

Yes?

Answer 3

When distributing the 3 you have to multiply it by each term.

Answer 4

So 3*4x=12x but is \[3*-2=-2\]?

Answer 5

Im so lost

Answer 6

Step 2 went from: \[3(4x-2) \to 12x-2\]

Answer 7

\[3(4x-2)\] Is the same as \[(3*4x) - (3*2)\]

Answer 8

So do you see now where the student made the mistake?