We have the equation negative 9

minus this whole expression, 9x minus 6– this whole thing

is being subtracted from negative 9– is equal to

3 times this whole expression, 4x plus 6. Now, a good place to start is

to just get rid of these parentheses. And the best way to get rid of

these parentheses is to kind of multiply them out. This has a negative 1– you

just see a minus here, but it’s just really the same thing

as having a negative 1– times this quantity. And here you have a 3

times this quantity. So let’s multiply it out using

the distributive property. So the left-hand side of

our equation, we have our negative 9. And then we want to multiply the

negative 1 times each of these terms. So negative 1 times

9x is negative 9x, and then negative 1 times negative

6 is plus 6, or positive 6. And then that is going to be

equal to– let’s distribute the 3– 3 times 4x is 12x. And then 3 times 6 is 18. Now what we want to do, let’s

combine our constant terms, if we can. We have a negative 9 and a 6

here, on this side, we’ve combined all of our like terms.

We can’t combine a 12x and an 18, so let’s

combine this. So let’s combine the negative 9

and the 6, our two constant terms on the left-hand

side of the equation. So we’re going to have

this negative 9x. So we’re going to have negative

9x plus– let’s see, we have a negative 9 and then

plus 6– so negative 9 plus 6 is negative 3. So we’re going to have a

negative 9x, and then we have a negative 3, so minus

3 right here. That’s the negative 9 plus

the 6, and that is equal to 12x plus 18. Now, we want to group all the

x terms on one side of the equation, and all of the

constant terms– the negative 3 and the positive 18 on the

other side– I like to always have my x terms on the left-hand

side, if I can. You don’t have to have them on

the left, so let’s do that. So if I want all my x terms on

the left, I have to get rid of this 12x from the right. And the best way to do that is

to subtract 12x from both sides of the equation. So let me subtract 12x from the

right, and subtract 12x from the left. Now, on the left-hand side, I

have negative 9x minus 12x. So negative 9 minus 12,

that’s negative 21. Negative 21x minus 3 is equal

to– 12x minus 12x, well, that’s just nothing. That’s 0. So I could write a 0

here, but I don’t have to write anything. That was the whole point of

subtracting the 12x from the left-hand side. And that is going to be equal

to– so on the right-hand side, we just are

left with an 18. We are just left with

that 18 here. These guys canceled out. Now, let’s get rid of

this negative 3 from the left-hand side. So on the left-hand side, we

only have x terms, and on the right-hand side, we only have

constant terms. So the best way to cancel out a negative

3 is to add 3. So it cancels out to 0. So we’re going to add

3 to the left, let’s add 3 to the right. And we get– the left-hand side

of the equation, we have the negative 21x, no other x

term to add or subtract here, so we have negative 21x. The negative 3 and the plus 3,

or the positive 3, cancel out– that was the whole

point– equals– what’s 18 plus 3? 18 plus 3 is 21. So now we have negative

21x is equal to 21. And we want to solve for x. So if you have something times

x, and you just want it to be an x, let’s divide by

that something. And in this case, that something

is negative 21. So let’s divide both sides of

this equation by negative 21. Divide both sides

by negative 21. The left-hand side, negative

21 divided by negative 21, you’re just left with an x. That was the whole point behind dividing by negative 21. And we get x is equal

to– what’s 21 divided by negative 21? Well, that’s just negative 1. Right? You have the positive version

divided by the negative version of itself, so it’s

just negative 1. So that is our answer. Now let’s verify that this

actually works for that original equation. So let’s substitute negative 1

into that original equation. So we have negative 9– I’ll do

it over here; I’ll do it in a different color than we’ve

been using– we have negative 9 minus– that 1 wasn’t there

originally, it’s there implicitly– minus 9

times negative 1. 9 times– I’ll put negative 1

in parentheses– minus 6 is equal to– well, actually,

let me just solve for the left-hand side when I substitute

a negative 1 there. So the left-hand side becomes

negative 9, minus 9 times negative 1 is negative

9, minus 6. And so this is negative 9

minus– in parentheses– negative 9 minus 6

is negative 15. So this is equal

to negative 15. And so we get negative 9– let

me make sure I did that– negative 9 minus 6,

yep, negative 15. So negative 9 minus negative 15,

that’s the same thing as negative 9 plus 15,

which is 6. So that’s what we get on the

left-hand side of the equation when we substitute x is

equal to negative 1. We get that it equals 6. So let’s see what happens when

we substitute negative 1 to the right-hand side

of the equation. I’ll do it in green. We get 3 times 4 times

negative 1 plus 6. So that is 3 times negative

4 plus 6. Negative 4 plus 6 is 2. So it’s 3 times 2,

which is also 6. So when x is equal to negative

1, you substitute here, the left-hand side becomes 6, and

the right-hand side becomes 6. So this definitely works out.

you make great tutorials, thanks.

you do a good job

I PASSED MY TEST BECAUSEE OF THIS.

@kalzorath guess what. shaddup

@MeHasComputer ?????

@MeHasComputer got something against math tutorials or something?

@spiritsoftheangel

@vishnuisme c =3 stupid

@vishnuisme C = 3

Dear Khan, please please please make a video about the huge differences between communism and socialism. Most Americans seem to misunderstand this subject, likely deeming it anti-american and probably a remainder of the policies during the vietnam war and all the propaganda involved.

What software is this?

Your voice makes me wanna shot my brains out

math is so overated were not going to be using it when we get older the only thing we should be worry about is money and all that

My brain just divided by zero

One of the best ways to make money is to get a good job. Two of the best fields for getting a job are Computer Science and Engineering. Both of those fields take LOTS OF MATH. Which you use every day. Basically, the more math you learn in school, the higher your paycheck will be. Look it up.

I always struggled with the Distributive Property. Appreciated.

how did you get the +6 to turn into a negative 6 without knowing that its a -1 at the start?

Can you subsctract 18 on that other side

I DID THAT WHOLE THING IN MY HEAD YESSSSS!~!!!!!!!!

math is a science without it no other science could exist

idiot.

i think ill pass math thanks to you

That's a joke right?

-_- to fast

Why does he always start da video," So we have the equation….."?

usually we subtracted the -21x +21 and another side 21 under +21 equal 42 then x=42

how you come up with -21 in first place, Pleas could you tell me . thanks

Why did you use -1? how come you did not used just a +1?

You helped me!

21

Fuck this

Do not read the comment below this

dude how many videos has he made?

this guy sounds like my guidance. named Dr blue

whay arbic sous-titres not available????

THIS GUY DOES EVERYTHING SO Differently!!

this man op so shut up

I have a great in two days. you just saved my life.

What about distribution property with exponents

Lol

I dont even know why im here right now

I paused the video straight away and tried to solve, but that invisible 1 really fucked me up at the start bro.

be my teacher!

very well explained

lol.. easy asf thanks khan academy.

I hate math

Please Help Me :''''( I Don't Under Stand a Bit!!!!!!!!!!!!

shoutouts to simpleflips

Thanks so much!!!! It really helped me with my homework. Thanks Sal😎

helpful but…..BORING he makes everything look so easy

this is helpful

You saved my life i would totallu sub but that is a social crisis waiting to happen but really though it really helped me do my work thanks!

Honestly, I hate math!!

I have a problem similar to this one but the answer don't show in the result

mkay

Omfgggg why can't I understand math it takes me way slower to comprehend math then other people I just don't know also don't know how I got straight B's😂

can you do something like 3−2(9+2m)=m cuz i i have no idea how to do it and im a math genius which says a lot

-9 is the smallest you would have to subtract it on both sides.. That’s how I was thought and will it work also?

he kind of sounds like Scott Disick

What is meant by distributive property

What is meant by combining like terms

What is the hidden number when there is a negative sign in front of parentheses

I challenge someone to count how many times he says "Equation"

Densmore?