-17 – x = -2(3x + 1)

- anonymous

-17 – x = -2(3x + 1)

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- anonymous

You need to distribute the -2 to each of the terms in the parentheses. Then you can solve it in the usual way.

- anonymous

i did that polPak and heres what i came up with

- anonymous

-21

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## More answers

- anonymous

Nope. What was the equation after you do the distributing?

- anonymous

-17 - 6x +6X -2-X

- anonymous

2(3X +1)
-17- X= 6X + 2

- anonymous

You forgot that it's a -2, not 2 you're distributing.

- anonymous

\[-2(3x + 1) = -2(3x) -2(1) = -6x - 2\]
So you should have
\[17 - x = -6x -2\]

- anonymous

oh so the 6 becomes -6x

- anonymous

And the 2 becomes -2.

- anonymous

Err My equation is slightly wrong..
You should have \[-17 -x = -6x -2\]

- anonymous

-17 - x = -6 - 2

- anonymous

Don't lose track of the x on the -6. It's important

- anonymous

then now i can solve for x
so the its
-17x -6 - 2

- anonymous

No. -17 - x is not -17x and you can't just put them together like that.

- anonymous

Ok look at it like this.

- anonymous

ok

- anonymous

You have this equation:
\[-17 - x = -6x -2\]
That means that \(-17 - x\) IS EXACTLY THE SAME AS \(-6x -2\)
So if they are the same then isn't \((-6x -2) + 2\) exactly the same as \((-17 - x) + 2\)?

- anonymous

-17 - 8 so there for x is 8

- anonymous

I have no idea what you are doing.. -17 - 8 doesn't enter into it.

- anonymous

i am just lost

- anonymous

Ok stop doing things.. Just look at what I'm saying.

- anonymous

\[-17 - x \text{ EQUALS } -6x -2\]

- anonymous

okay lol i am stopping right now

- anonymous

Ok? They are the same.

- anonymous

That's what equals means right?

- anonymous

yes

- anonymous

Ok so now lets use some basic arithmetic rules to clean this up a bit.
First we can swap the terms on the left because addition can be rewritten in any order and it works the same..
\[-17 -x = -x -17\] right?

- anonymous

okay

- anonymous

Do you agree that those two are equal? Is 3+5 the same as 5+3 and -3 - 5 the same as -5 - 3?

- anonymous

yes

- anonymous

because you distribute right

- anonymous

Commute, but yeah.

- anonymous

Ok, so -17 - x is the same as -x - 17.
But we also said that -17 - x was the same as -6x - 2.
So that means that -x - 17 must be the same as -6x - 2.

- anonymous

Right?

- anonymous

right

- anonymous

So now our equation looks like this:
\[-x - 17 = -6x - 2\]

- anonymous

that part i got is solving for x thats has me upside ways

- anonymous

We'll get there.

- anonymous

So if those two things are the same.. Then isn't \[6x + (-x - 17) = 6x + (-6x - 2)\]

- anonymous

Because we added 6x to both sides, and if they were equal to start with, they must still be equal.

- anonymous

okay thats the part that throws me off

- anonymous

How so?

- anonymous

its like my flipping mind goes blank and i have no idea what comes next

- anonymous

Ok relax for a second and lets talk about something else first.

- anonymous

or maybe i am trying too hard to understand and i get tied up

- anonymous

Think of a number, any number you want. Don't tell me what it is.

- anonymous

ok

- anonymous

Now, tell me what 2 times that number is.

- anonymous

184

- anonymous

Ok. So now I will magically read your mind and tell you that your number is 92!

- anonymous

How did I accomplish this sorcery?

- anonymous

lol yes

- anonymous

you divided

- anonymous

But how does that help me?

- anonymous

Because you told me that 2x = 182

- anonymous

Well I know that if 2x = 182 then \[2x \times {1 \over 2} = 182 \times {1 \over 2}\]

- anonymous

so you have to find out what 2x amounts to

- anonymous

Because you said that they were the same, so anything I do to both sides will maintain equality.

- anonymous

And \[2x \times \frac{1}{2} = x\]

- anonymous

And \[182 \times \frac{1}{2} = 92\]

- anonymous

So therefore x = 92

- anonymous

So now I'm thinking of a number.

- anonymous

91

- anonymous

okay

- anonymous

Whoops. Sorry I typo'd your response.

- anonymous

Shoulda been 184 not 182.

- anonymous

no one has ever broke it down like this thank you

- anonymous

its okay

- anonymous

so you want me to solve for your number

- anonymous

Now if you take the number I'm thinking of, and add 17 to it. You will get 2 more than 6 times that same number.

- anonymous

So first. can you write an equation (using x for my number) which describes the statement I've given you?

- anonymous

2(6^6)+17=X

- anonymous

Not quite. Lets break down what I said:
x + 17
The number I'm thinking of, and add 17 to it
=
IS
2 more than 6 times that number
2 + 6x

- anonymous

Or better still
6x + 2

- anonymous

12(6)=72+17=89

- anonymous

No no no.

- anonymous

OH WOW

- anonymous

You keep jumping ahead ;)

- anonymous

okay am slowing down

- anonymous

and laughing at myself

- anonymous

np =)

- anonymous

Try again.
14 more than the number is 2 more than 4 times the number.

- anonymous

We're just practicing turning english into equations.

- anonymous

okay

- anonymous

Don't try to solve it yet. Just rewrite what I say in equation form.

- anonymous

Actually 14 more than the number is 5 more than 4 times the number.

- anonymous

14 + n = 2(4)

- anonymous

Sorry

- anonymous

Almost!

- anonymous

was i close

- anonymous

The left side is right, the right side is not.

- anonymous

Try my last version, but break it down a bit.
If x is my number what is 4 times my number??

- anonymous

14 + n = 5(4 + n) oh please be right

- anonymous

You're doing great btw. It's important to have patience when working through this.

- anonymous

No, that's not right still. Lets work through it a little at a time.

- anonymous

What is 4 times my number?

- anonymous

your number is 14 right

- anonymous

no

- anonymous

my number is x

- anonymous

ok am gonna shoot here is it 14x be gentel

- anonymous

lets do something really quick cause it seems like we have a breakdown when you try to use letters instead of numbers.
If I tell you my number is 22, and I ask what is 2 times my number what would you do?

- anonymous

2(22)=44

- anonymous

Awsome!

- anonymous

That's perfect

- anonymous

Now if I tell you my number is k and I ask you what's 4 times my number what would you do?

- anonymous

yeah me finally

- anonymous

4(k)

- anonymous

yep!

- anonymous

And if I tell you my number is b and I ask what is 5 more than (4 times my number)?

- anonymous

You taking a long time, so I know something is wrong ;p

- anonymous

If I tell you my number is 3 and I ask what is 5 more than my number?

- anonymous

oh help me okay it would 20(b) or 5(b)=20

- anonymous

neither.

- anonymous

darn it

- anonymous

it's just a little language barrier. We'll fix it

- anonymous

If I tell you my number is 3 and I ask what is 5 more than my number what would you do?

- anonymous

am trying not to think of the words

- anonymous

the words are important.

- anonymous

3(5)=15

- anonymous

15 is 3 more than 5?

- anonymous

Or 5 more than 3?

- anonymous

What is 5 more than 3?

- anonymous

8

- anonymous

5 + 3

- anonymous

am adding here

- anonymous

5 + 3 means 5 more than 3

- anonymous

gosh i feel stupid now

- anonymous

It's ok. Just a little gap in your knowledge.

- anonymous

so am mixing up more with multiplying

- anonymous

a huge gap

- anonymous

Right. If I say 4 times my number is 4k Then what is 5 more than 4 times my number?

- anonymous

ok let me solve it

- anonymous

Don't have to solve, just have to translate.

- anonymous

4k +9

- anonymous

So close!

- anonymous

oops i left off the 4

- anonymous

No.

- anonymous

Ok, my number is k. What is 4 times my number?

- anonymous

4(k)=4k

- anonymous

Ok, and what is 5 more than 4 times my number?

- anonymous

You already solved half of this just a minute ago.

- anonymous

9(n)

- anonymous

holding my breath

- anonymous

No. it's
5 + 4k
5 more than four times my number

- anonymous

5 + 4k

- anonymous

5 more means +5

- anonymous

am trying too hard

- anonymous

yes

- anonymous

Ok, but now you know.

- anonymous

okay so i don't add 5 and 4 just 5+ 4k

- anonymous

right

- anonymous

these are the steps.
-17-x=-6x-2
6x-x=17-2
5x=15
x=3

- anonymous

While I'm sure doing her work is appreciated it's not going to help her on the next problem.

- anonymous

awe man

- anonymous

thats true

- anonymous

thanks pat18

- anonymous

One sec Bella. This thread is lagging up a bit. Lets start a new question with the next one?

- anonymous

okay

- anonymous

brb

- anonymous

you are welcome.

- anonymous

okay am back polPak

- anonymous

Can you make a new questiON?

- anonymous

err question?

- anonymous

okay

- anonymous

what is 6 times my number a and 8 more times 4

- anonymous

Oh, sorry I think you misunderstand. I am going to make a new problem on the left side. Please go there

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