12x-3(2x+7)=-45 could someone walk me through this

- anonymous

12x-3(2x+7)=-45 could someone walk me through this

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- schrodinger

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- anonymous

You want to try and get the x on one side and the anything else on the other.

- anonymous

So I would start with distributing the 3 through that quantity...

- anonymous

Okay, so we start off by distrubiting the '-3' to the (2x+7). -3*2x = -6x; -3 * 7 = -21
This leaves us with:
12x -6x -21 = -45
We group like terms:
ie. 12x-6x = 6x;
We're left with 6x-21=-45, so lets add 21 to both sides. 6x-21+21 = -45+21
This simplifies to: 6x = -24; we now divide by 6
x = -4.
Done!

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- anonymous

-3(2x+4)=5(3-2x) mind helping me again

- anonymous

tlk to me like im a 5 yr old lol

- anonymous

Without just giving you the answer, it's always best to try yourself. That's the way you learn. So we need to distribute again, i.e multiply the -3 through and the 5 through.

- anonymous

ok -6x+4=15-10x

- anonymous

first step right?

- anonymous

Not quite. I think you had the right process because you used it on the right side correct. You forgot to multiply the 4 by -3.

- anonymous

wait

- anonymous

i just caught it

- anonymous

so -6x+12=15-10x

- anonymous

Minus 12 :) So -6x-12=15-10x

- anonymous

see this where i get confused when do i need to change signs

- anonymous

Ok since the first time you are multiplying by -3 anything positive becomes negative.

- anonymous

when i need to change from addition to sub

- anonymous

i understand that but like on a 2 or 3 step prob when do i change the operation

- anonymous

I'm not quite sure what you're asking. I would need an example...

- anonymous

im really pretty intelligent i promise....lol

- anonymous

let me find an example

- anonymous

Math is not everyone's thing. I just happen to be good at it. :) Music, on the other hand, I only listen to it.

- anonymous

ok

- anonymous

Here's a few more examples of "changing the sign". I'm not sure I understand what you're asking so maybe you will see the pattern yourself.
3(7x+2) = 21x+6 --- A positive * a positive is a positive.
-3(3x+2) = -9x-6 --- A negative number * a positive is a negative.
5(-2x-1) = -10x - 5 --- A positive number * a negative is a negative.
-7(8x-4) = -56x + 28 --- The first part is a negative * a positive = negative, but the second is a negative times a negative which is a positive.
Can you try simplifying:
-3(-4x+7) = ???
for me?

- anonymous

6x+9-4x=3x+11

- anonymous

12x+-21?

- anonymous

Yep!
If it helps you to think of it as "Twelve x plus negative 21" then by all means leave it like that.

- anonymous

As for the problem you posted above, first, let's simplify the left side by adding like terms.
Then try adding something to both sides to get the x's on one side. Then add another something to get the "numbers" on the other side. Then divide by the number in front of the x to get your final answer.

- anonymous

10x+9=3x+11 or 13x=20 cani combine both sides of the = sign at once?

- anonymous

wait i just read what u wrote

- anonymous

6x+9-4x=3x+11
5x+9=11?

- anonymous

You can if you can keep track in it -- with no offense met, I'd practice doing them individually for at least a week of classes. When you've got it down pat feel free to add on steps in your head. Eventually you'll reach a point where you can solve 6x+9-4x=3x+11 all in your head.
You made a mistake in your answer though:
Left hand side first: 6x+9-4x = 2x + 9; You added 4x in an attempt to kill the -4x, but if you're going to do that you must do that to both sides. It is far easier just to do "6x-4x = 2x"
Now the left side: Oh wait! It's already done! "2x+9"
So we have 2x+9 = 3x +11;
Subtract 2x from each side ---> 2x+9-2x = 3x-2x+11 ----> 9 = x+11
Now lets subtract 11 from each side leaving: -2 = x;
You can then check the answer

- anonymous

Are you able to follow what I did? If you'd like I can give another example, but can you explain your thought process for me as you solve it?

- anonymous

Here's a problem I just made up if you'd like to try again: -5(3x+1) = 16x-3

- anonymous

-15x+1=16x-3

- anonymous

Make sure to distrubute the "-5" to everything in the parantheses.

- anonymous

-15+-1=16x-3

- anonymous

so combine right

- anonymous

so when one distrubutes you take the number outside of the parentheses and multiply it by each of the (inside terms). so you are doing: -5 * 3x; AND -5 * 1;
so we have -15x -5 (or in your preffered notation: -15x + -5)

- anonymous

We can come back to distrubution later if you'd like:
-15x + -5 = 16x + -3 is where we can pick this up again. Do this out but tell me in words what you're doing as well please. I want to see what you're thinking haha. Cheers for sticking with this btw.

- anonymous

then we combine the x's together so mobve the smaller x to both sides?

- anonymous

trust me id rather b watching family guy,,,lol

- anonymous

Yep. So yeah, add the Opposite of the smaller x value to both sides.

- anonymous

-15x+-5=16x+-3
-15x+-5=-15x+-3
x=-5=1x+-3?

- anonymous

Also, I was asleep when making this example: The end result will be a fraction, my mistake.

- anonymous

no worries

- anonymous

Errr, okay, so explaint to me how you went from: -15x+-5=16x+-3 to
-15x+-5=-15x+-3

- anonymous

wait wait sorry

- anonymous

As a reminder, our first goal is to get rid of the x's from the left hand side. The way we do this is by adding the opposite of them to it. Anything + the opposite of anything = 0; Anything + -Anything = 0.

- anonymous

(and when we add anything (completely new) to one side, we must do it to the other).

- anonymous

-15x+-5=16x+-3
15x=-15=16x+-3....so 20=16x+-3...not done but thats how i do the first side right

- anonymous

u with me or u fall asleep again

- anonymous

I'm not sure what you did there? Both sides are (by themselves) as simplified as you can get them without adding completely new things to the equation.
Let's do this: 3x+2 = 4x+1
Each side is as simplified as possible: Let's get the x's over to the right.
If I add -3x to both sides (which is the opposite of the the left hand side term), we get:
3x-3x+2 = 4x+1-3x ---> 3 = 4x+1.
Now using this example, try doing
-15x + -5=16x + -3
again. Also, remember you can not add a variable, the "x's" to the constants "the numbers".

- anonymous

Now using this example as a refrence, try doing* (correction to the above)

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