3(2+x)=12

- anonymous

3(2+x)=12

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- zzr0ck3r

divide both sides by 3, and you have what?

- ellamallow

First you would multiply 2 and x by 3 and you would get (6+3x)=12

- zzr0ck3r

I think it is easier to divide both sides by 3, then you have x+2=4

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## More answers

- zzr0ck3r

but either way works :)

- ellamallow

Well that is not how I was shown to do it.. But yeah I guess...

- anonymous

Wait what?!?!?!

- ellamallow

|dw:1441152865714:dw|

- anonymous

After the 3x =6 what do i do

- ellamallow

divide 3x AND 6 by 3 to get x by itself, then you get the answer. x= ?

- anonymous

X=3??

- anonymous

I'm so confused

- zzr0ck3r

This is how I would do it.
\[3(x+2)=12\]
We want to get \(x\) by itself on one side. Firsts I would divide away the \(3\)
\[\frac{3(x+2)}{3}=\frac{12}{3}\\\frac{\cancel{3}(x+2)}{\cancel{3}}=4\\ \\x+2=4\]
Now we want to subtract \(2\) from both sides, so that \(x\) is by itself.
\[x+2-2=4-2\\x=4-2\\x=2\]

- ellamallow

sorry, my handwriting on the computer is horrible as well, that didn't help.

- anonymous

Omg Thats worse! I'm so lost! Sorry guys ๐ฉ

- ellamallow

Okay, sorry. I really tried to help >.<

- anonymous

Its okay I appreciate it so much

- anonymous

Hi! I'm pretty new but I might be able to help... What you're looking at there in this equation is something called "Distributive property." see the 3(2+x) ? Thats' it! That's going to be the key to this problem. It gets its name from having to distribute whatever number is outside the parentheses. In this case, you would distribute the 3 into the 2, and the x. So take your three, and the two. Multiply them together. What do you get? 6. Now, do the same with the x.

- anonymous

Okay i get 3 if I do 3* X

- zzr0ck3r

Which part of my explanation are you confused by?

- anonymous

All of it

- anonymous

Yep! Perfect! Do you know what you get when you multiply 3 and x together?

- anonymous

3 because x = 1

- anonymous

I know that stuff but writing it out is confiding me

- zzr0ck3r

it is not that \(x=1\) it is \(x=1x\)

- anonymous

Not quite... In this case, we won't be treating it as a 1, instead we will treat it as just a plain x. In this case, all you would need to do is put a three next to the x! So you would end up with 3x : >

- zzr0ck3r

@enderkitty29 some people like to think if there being a 1 in front of an x when there is no coefficient.

- anonymous

Okay can you show how i would write that please

- anonymous

So far i have
3(2+x)=12
6+3 = 12

- anonymous

Ah, you're very right zzr0ck... Forgot to take into account the other ways of looking at the problems.

- anonymous

Wait a minute Kaitlyn, there is something a bit off about what you have so far. You are missing an x in the equation! Do you know where it should be?

- anonymous

3x?

- anonymous

Perfect! The x is a very important part of the equation. Without it, you won't be able to solve it : )

- anonymous

Okay what is the next step

- anonymous

Now, we want to try and get the x all by itself! In this case, we must subtract something from both sides. What do you think we should subtract?

- anonymous

What happens to that 3 on the outside of the ()

- anonymous

3? From 12 and

- anonymous

The three is no longer there, since you multiplied the two numbers by three inside the parentheses. It's almost like canceling it out, so you don't need to worry about it anymore :)

- anonymous

Okay so I subtract 3 from 3x and 12?

- anonymous

Nope, not the three. Make sure to remember your equation is 6 + 3x = 12.

- anonymous

We are trying to get the x all by itself first. What do you need to take away from the left side of the equation to do this?

- anonymous

So? 6?

- anonymous

Perfect! Since you are going to subtract the 6 from the left side, you need to do this to the right side. What does our equation look like now?

- anonymous

3(2+x)=12
6+3x =12
-6 -6

- anonymous

Perfect! So far, we should end up with 3x = 6

- anonymous

Do you understand why its 6 on the right side?

- anonymous

Because whatever you do to one side you do to the other

- anonymous

Right on! Now, only one more step. Almost done. Do you see the 3x? That means 3 * x

- anonymous

We still need the x by itself, so we need to get the three out of there somehow. Do you know how to do that?

- anonymous

6รท3?

- anonymous

Wonderful job! Thats correct!

- anonymous

So what do we end up with overall? What does our equation look like now?

- anonymous

X=2?

- anonymous

Yep! You got it! There is your answer : )

- anonymous

Omg thank you!!!! Of its not to much to ask i need one more to be finished

- anonymous

I can totally help!

- anonymous

Thank you!!!
5-2(x-4)=20

- anonymous

Alright! Remember the thing we did in our last equation called distributive property? We are going to do that here again! What do you think we should do first?

- anonymous

Subtract 2 on each side?

- anonymous

Nope! I'll give you a hint. It has to do with the -2(x-4).

- anonymous

Or 4

- anonymous

Remember what we did last time with the distributive property : )

- anonymous

You add 4

- anonymous

Nope! -2(x-4). What do we do with the negative two?

- anonymous

Multiply

- anonymous

Yeah! What are we going to multiply?

- anonymous

-2

- anonymous

Wonderful! So lets take the -2 and the x, and multiply them together. What do we get?

- anonymous

-2x?

- anonymous

Yeah! Now lets do -2 and -4.

- anonymous

-6?

- anonymous

Nope! Multiply them together, don't add. Remember what happens when you multiply two negatives with each other : )

- anonymous

It becomes a positive?

- anonymous

Right on! So what is -2 * -4 then?

- anonymous

8

- anonymous

Yep! So what does our equation look like now that we distributed the -2?

- anonymous

5-2(x-4)=20
2x + 8 =20

- anonymous

You forgot two things! First, you forgot to keep the 5 in the equation : ) Second, there should be a negative in front of the 2x. So, our equation should look like this: 5 - 2x + 8 = 20

- anonymous

Got it?

- anonymous

Oops yeah

- anonymous

No worries, lets move on! Now, we will be doing something called "Combining like terms." This means to take numbers that are similar, and add them together! Do you see any similar numbers here?

- anonymous

5? 8?

- anonymous

Perfect! Now add those together, and what do you get?

- anonymous

13

- anonymous

So how would i write that down

- anonymous

Okay, good. Now that we added the 5 and 8 together, we are going to have 13 - 2x = 20

- anonymous

13 - 2x = 20 (it got cut off a bit, had to rewrite it)

- anonymous

Do you understand why we added them together and got what we got?

- anonymous

Yes because we are trying to get x alone

- anonymous

Perfect! What do you think we should do next?

- anonymous

13-20? Or 2x-20

- anonymous

20 - 13 : )

- anonymous

After that, what does our equation look like?

- anonymous

-2x=20

- anonymous

Oops nope

- anonymous

-2x = 7

- anonymous

Yep! There we go. What do we do now?

- anonymous

2รท7

- anonymous

Perrrrrfect! Now, you can either leave it as 7/2 or 4.5

- anonymous

What does the paper say?

- anonymous

I for 3.5

- anonymous

I got 3.5

- anonymous

Yep! 3.5 That's what I ment lol. Finger slipped : )

- anonymous

Its Okay Omg thank you so much!!!!!!!

- anonymous

You're very welcome! You're a very fast learner : ) Keep up the good work and glad I could help!

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