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

step 1: 2(3x − 4) = 8 + 2x + 4
step 2: 5x − 6 = 12 + 2x
step 3: 5x − 2x = 12 + 6
step 4: 3x = 18
step 5: x = 6

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

step 2; 6x − 6 = 2(6 + x + 2)
step 2; 6x − 8 = 12 + 2x
step 3; 5x − 2x = 12 − 6
step 3; 5x + 2x = 12 + 6

2. the steps below show the incomplete solution to find the value of m for the equation 4m − 2m + 4 = −1 + 13:

step 1: 4m − 2m + 4 = −1 + 13
step 2: 4m − 2m + 4 = 12
step 3: 2m + 4 = 12

which of these is most likely the next step?

2m = 3
2m = 8
2m = 16
2m = 18

3. how many solutions does the equation 4n + 6 = 4 + 2 + 4n have?

two
many
none
one