Question

(07.05 HC)

The incorrect work of a student to solve an equation 2(y + 8) = 4y is shown below:

Step 1: 2(y + 8) = 4y
Step 2: 2y + 10 = 4y
Step 3: 2y = 10
Step 4: y = 5

Which of the following explains how to correct Step 2 and shows the correct value of y? (5 points)

Select one:
a. The equation should be y + 8 = 4y after division by 2; y = 4
b. The equation should be y + 8 = 4y after division by 2; y = 6
c. 2 should be distributed as 2y + 16; y = 4
d. 2 should be distributed as 2y + 16; y = 8

Answer 1

D

Explanation:

1. The equation actually goes: 2(y+8)=4y
2. 2y+16=4y
3. -2y -2y (must minus 2y from both sides)
4. 16=2y
5. divide both sides by 2
6. Y=8

Answer 2

D. 2 should be distributed as 2y + 16; y = 8

Explanation:

We have
`2(y+8)=4y` we are going to solve it step by step:

1.
`2(y+8)=4y`

2. We have to distribute 2, then:

`2y+16=4y`

3. Now we have to sum (-2y) in both sides of the equation:

`2y+16-2y=4y-2y\\16=2y`

4. Finally we have to divide both sides of the equation in 2:

`16=2y\\\\(16)/(2)=(2y)/(2)\\ 8=y`

Then the correct answer is option D, in step 2: 2 should be distributed as 2y+16, and resolving the equation we obtain that y=8 .