Question

Okay guys, last question. I promise, I am just studying for a Math test that is coming up.

Solve the following equation:

-4y+8=4(2y-2)-2(-16+8y)

A) y=-4
B) y=4
C) y=-2
D) y=-6

Answer 1

Use Distributive Property to get rid of all the parenthesis on the right first.
a(b + c) = ab + ac.
Do the step and I will help you with the next step.

Answer 2

Okay, I understand what the distributive property is. The only problem is I don't see where I can start with that in this equation. Do I have to do what is inside the ( ) first?

Answer 3

You have 4(2y-2). You can use distributive property there.
You also have -2(-16+8y) where you can use distributive property again.

Answer 4

Okay, so should I use distributive property on both of them like this?

-4y+8=8y-8-32-16y

Is that right?

Answer 5

You are almost correct. Check the sign of 32. Should it be -32 or +32?

Answer 6

+32 I believe.

Answer 7

Correct. So you have -4y + 8 = 8y - 8 + 32 - 16y

Next bring all the y terms to the left of the equal sign and take all the constant terms to the right of the equal sign. Note: Switch signs when you take a left hand side term to the right or when you take a right hand side term to the left. For example, 5x - 2 = 3x + 6 can be written as 5x - 3x = 6 + 2. Do the same for the above equation.

Answer 8

So are you saying that I should switch the equation vise versa before I do this part?

Answer 9

We want to solve for y. So we are gathering up all the y terms on the left and all the constant terms on the right.

Answer 10

-4y+8=8y-8+32-16y
-4y+8=8y+32
-8
-4y=8y+32

Right so far? Or no?

Answer 11

Not correct. Okay it looks like you are used to doing it the long way. First I will take an example and do it the long way. Then I will do the same the easier way.
Example: 5x - 2 = 3x +6
To get rid of the -2 on the left, add +2 to both sides:
5x -2 = 3x + 6
+2 = + 2
5x = 3x + 8
To get rid of 3x on the right subtract 3x from both sides:
5x = 3x + 8
-3x -3x
2x = 8
x = 4.

Answer 12

Now I will show you the easy way to solve 5x - 2 = 3x + 6
Bring the x terms to the left and constant terms to the right. When you switch sides, simply remember to change the sign. So a 3x on the right when taken to the left will become -3x and a -2 on the left when taken to the right will become +2.
So 5x - 3x = 6 + 2
2x = 8
x = 4.

Answer 13

Hmmmm, I do admit that I am used to doing it the long way. I am not familiar with doing it the easy way.

Answer 14

Okay, if you stll prefer to do it the long way then proceed with where we left off:
-4y+8=8y-8+32-16y
On the right you can simplify first by adding or subtracting the like terms

Answer 15

Okay, I prefer to do that because nobody really ever showed me the easy way. If they did, I must have not been paying attention.

Anyways..

-4y+8=8y-8+32

So that is done.

Answer 16

No. not yet done.
You have to watch for the signs carefully.
On the right we had 8y-16y = ?
Also on the right we have -8 + 32 = ?

Answer 17

Okay, well -8+32=24
and wouldn't 8y-16y=-8y

So then wouldn't we be at -4y+8=-8y+24?

Answer 18

Excellent!
Now do your long way and solve for y.

Answer 19

Subtract 8 from both sides of the equation first.

Answer 20

-4y+8=-8y+24
-8 -8
-4y=-8y+16

Am I still on track?

Answer 21

Yes!
What should be the next step?

Answer 22

Well don't we still have to isolate y?

Answer 23

Yes.

Answer 24

Okay, so that is the next step I do believe. The only problem is that there is still a y on both sides of the equation. That does not seem right.

Answer 25

Add 8y to both sides to get rid of the y term on the right.

Answer 26

Okay, so like this?

-4y=-8y+16
+8y +8y

4y=16

4y/4=4 16/4=4

I think I got the answer, the answer is 4! :D

Answer 27

Excellent!

Answer 28

But if you learn to do it the easy way the whole problem can be done in just 5 lines. It will save you a lot of time doing homework and taking tests. So here it is:
-4y+8=4(2y-2)-2(-16+8y)
-4y + 8 = 8y -8 + 32 - 16y
-4y - 8y + 16y = -8 - 8 + 32 4y = 16
y = 4

Good luck!

Answer 29

Okay, good stuff. I will have to study the easy way now, I just have been so used to doing these problems the long way. Thanks for actually spending all of this time on helping me out, I owe you a huge thank you sir. Anyways, thank you and have a good night!

Answer 30

You are welcome. Good night.