Question

9.
Which of these is a simplified form of the equation 6y + 4 = 8 + 2y + 2y? (5 points)


6y = 8
10y = 12
2y = 4
4y = 12
10.
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? (5 points)



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

Answer 1

9.
6y+4=8+2y+2y
Combine like terms
6y+4=8+4y
Get like terms on the same side, subtract 4 from both sides to get
6y=4+4y
Subtract 4y from both sides to get
2y=4 IS the answer (even though it can be simplified further, that answer isn't one of the choices so 2y=4 is the equation simplified.)

10.
Step 2 was the mistake when you distribute a number you don't add (which is what they did to get 5x) you multiply to get 6x. So the correct step 2 would be
6x-8=12+2x
Becuase of the distributive property.

Hope this helped!

Answer 2

Question 9:

6y + 4 = 8 + 2y + 2y

6y + 4 = 8 + 4y

6y - 4y = 8 - 4

2y = 4

y = $\frac{4}{2}$

y = 2

Hence, the answer is C.

Question 10:

2(3x – 4) = 8 + 2x + 4

6x - 8 = 12 + 2x

6x - 2x = 12 + 8

4x = 20

x = $\frac{20}{4}$

x = 5

Hence, the answer is B.