Welcome to level one

linear equations. So let’s start

doing some problems. So let’s say I had the equation

5– a big fat 5, 5x equals 20. So at first this might look

a little unfamiliar for you, but if I were to

rephrase this, I think you’ll realize this

is a pretty easy problem. This is the same thing as

saying 5 times question mark equals 20. And the reason we do the

notation a little bit– we write the 5 next

to the x, because when you write a number right

next to a variable, you assume that you’re

multiplying them. So this is just

saying 5 times x, so instead of a question

mark, we’re writing an x. So 5 times x is equal to 20. Now, most of you all could

do that in your head. You could say, well, what

number times 5 is equal to 20? Well, it equals 4. But I’ll show you a way to do

it systematically just in case that 5 was a more

complicated number. So let me make my pen

a little thinner, OK. So rewriting it, if

I had 5x equals 20, we could do two things

and they’re essentially the same thing. We could say we just divide

both sides of this equation by 5, in which case, the left

hand side, those two 5’s will cancel out, we’ll get x. And the right hand side,

20 divided by 5 is 4, and we would have solved it. Another way to do it, and this

is actually the exact same way, we’re just phrasing

it a little different. If you said 5x equals 20,

instead of dividing by 5, we could multiply by 1/5. And if you look at that, you can

realize that multiplying by 1/5 is the same thing

as dividing by 5, if you know the difference

between dividing and multiplying fractions. And then that gets the

same thing, 1/5 times 5 is 1, so you’re just

left with an x equals 4. I tend to focus a

little bit more on this because when we start having

fractions instead of a 5, it’s easier just to think about

multiplying by the reciprocal. Actually, let’s do one

of those right now. So let’s say I had negative

3/4 times x equals 10/13. Now, this is a harder problem. I can’t do this one in my head. We’re saying negative

3/4 times some number x is equal to 10/13. If someone came up to you on

the street and asked you that, I think you’d be like me,

and you’d be pretty stumped. But let’s work it

out algebraically. Well, we do the same thing. We multiply both sides

by the coefficient on x. So the coefficient, all that

is, all that fancy word means, is the number that’s

being multiplied by x. So what’s the

reciprocal of minus 3/4. Well, it’s minus 4/3 times,

and dot is another way to use times, and

you’re probably wondering why in algebra, there

are all these other conventions for doing times

as opposed to just the traditional

multiplication sign. And the main reason is, I think,

just a regular multiplication sign gets confused

with the variable x, so they thought of either using

a dot if you’re multiplying two constants, or just writing

it next to a variable to imply you’re

multiplying a variable. So if we multiply the left

hand side by negative 4/3, we also have to

do the same thing to the right hand

side, minus 4/3. The left hand side, the

minus 4/3 and the 3/4, they cancel out. You could work it out on

your own to see that they do. They equal 1, so we’re just

left with x is equal to 10 times minus 4 is minus 40, 13 times

3, well, that’s equal to 39. So we get x is equal

to minus 40/39. And I like to leave

my fractions improper because it’s easier

to deal with them. But you could also view

that– that’s minus– if you wanted to write it

as a mixed number, that’s minus 1 and 1/39. I tend to keep it like this. Let’s check to make

sure that’s right. The cool thing about algebra is

you can always get your answer and put it back into

the original equation to make sure you are right. So the original equation

was minus 3/4 times x, and here we’ll substitute

the x back into the equation. Wherever we saw x, we’ll

now put our answer. So it’s minus 40/39, and

our original equation said that equals 10/13. Well, and once

again, when I just write the 3/4 right next to

the parentheses like that, that’s just another

way of writing times. So minus 3 times minus

40, it is minus 100– Actually, we could do

something a little bit simpler. This 4 becomes a 1

and this becomes a 10. If you remember when you’re

multiplying fractions, you can simplify it like that. So it actually becomes

minus– actually, plus 30, because we have a minus times

a minus and 3 times 10, over, the 4 is now 1, so all

we have left is 39. And 30/39, if we divide the

top and the bottom by 3, we get 10 over 13, which

is the same thing as what the equation said

we would get, so we know that we’ve got

the right answer. Let’s do one more problem. Minus 5/6x is equal to 7/8. And if you want to

try this problem yourself, now’s a

good time to pause, and I’m going to start

doing the problem right now. So same thing. What’s the reciprocal

of minus 5/6? Well, it’s minus 6/5. We multiply that. If you do that on

the left hand side, we have to do it on the

right hand side as well. Minus 6/5. The left hand side, the

minus 6/5 and the minus 5/6 cancel out. We’re just left with x. And the right hand

side, we have, well, we can divide both

the 6 and the 8 by 2, so this 6 becomes negative 3. This becomes 4. 7 times negative

3 is minus 21/20. And assuming I haven’t

made any careless mistakes, that should be right. Actually, let’s just

check that real quick. Minus 5/6 times minus 21/20. Well, that equals

5, make that into 1. Turn this into a 4. Make this into a 2. Make this into a 7. Negative times

negative is positive. So you have 7. 2 times 4 is 8. And that’s what we

said we would get. So we got it right. I think you’re

ready at this point to try some level one equations. Have fun.

thank you so much!!!

thx

He makes it harder to understand

Khan academy is annoying

I would have loved it if he started with "What makes an equation linear?"

Thanx a lot just learned that first one after you just wrote it down lol

Can you do this? Plz I am almost to testing in 7th grade and 8th so plz help me with this? 14-x= 6; 4,6,8?

Needed a bedtime story

Math ASMR

okay but at the fact when this video came out I was two years old wHAt—

You don't explain properly

You are bluddy amazing!

13 year anniversary since this was updloaded

this shank doesnt make any since

It takes replay to understand guys

Helps…👍

everyone, just think of it as removing the coefficent (number part) from the variable part (x,y,z, blah blah). The variable part needs to be alone. The purpose of linear equations are to find the x and y coordinates to plot in graphs. The variable part determines the x and y coordinates. Hope that helped.

I thought YouTube would do a better job at explaining this than my teacher but I was wrong. Both of them make zero sense. I have a math final tomorrow and I have zero clue what we learned this entire year I haven’t understood anything in math this entire year cause my math teacher is horrible at teaching. I am not the only kid who has this problem it’s actually because my math teacher sucks.

My solution is more faster and easier than his…it just take 10 seconds

In the class l understand but when it's time for exam even tho I studied l fail 😭😂😄

"That's a big fat five"

Me: That's what she said.

5×4=20

im ok .

I wish math never existed!! 😩😩😭

Sorry iam kiding u explain properly

2018 anyone?

5:44 you could’ve also simplified 3 and 39 too

Sir main ne algebra kabhi nahi shikha hai

To ab main kaise shikhu

Sal do you have ligma?

Sir plz reply me

Who watching in 2018 2006 we should have known this already !!

Khaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaan

Why do you have to switch the fraction in the second question?

Mr.khan our entire university reccomend your video.

Why does math exist

You ruined my 7th-8th grade year

Same here

me:

what is 5 + imes?#youcanlearnanything ?

#noicant

When will I ever need to use this stuff

N

keep in mind that we are most likely not going to be doing variables when we are getting food for our families… or when we get robbed, or when we are doing any thing… unless you become a teacher

my surname is Khan

when u need to pass algebra class somehow

didnt help me

if i die with doing math i will be in the heaven

Ok

guys are you aware that when a university burns all of it student will automatically have the bachelor

Kahn is the Bob Ross of Math

I was 4 in 2006

I LUV THIS CHANNEL

It's 2018 and I'm here because I couldn't understand it in school 5 years ago and it still bothers me so I decided to end this and understand it. I'm also wearing all Hollister now because my clothes were lame back then and I was always jealous of the people with nice clothes..

Why is maths soo hard ?????

Why did he divide by 2 the -6 over 5 and the 7 over 8 ?? He divided by 2 so he got -3 from -6 and 4 from 8, but why didn’t he do that with the first equation? The -3 over 4 x = 10 over 13? Why didn’t he divide those by 2 ? Can anyone explain please.

I’m just here cause I don’t pay attention in class

So you do everything in reverse order? If the equation says times you divide and if it says addition do subtraction? And you do BEDMAS in reverse order too? ╮(￣▽￣"")╭

This is a good prank

Read more

Me after watching this:😓😢😦😧😭😭😭😭

Can anyone help me?

My question is

-4 -2v + 8 = 6 – 6 – 9v + 6v

Anyone got a solution?

The sad part is teachers are supposed to teach us and yet we have to go the many different sites to learn everything they were supposed to teach us.

I'm in 7th grade doing Algebra I, all you need to do is practice equations, and you'll get it down.

Anyone 2019?

Soo hard 😭😭😭 tomorrow is periodic exams

Watching 2019

lol this 12 year quality is burning my eyes but i'm being patient and watching cuz Khan Academy

Wish you could have better video quality

Thanks math teacher

This suddenly got easy

Who is watching this in 2020?

i understand love this channel

This video is almost 14yo! Excellent.

This is really helpful man!

Esam El-emam that's what I am doing

Is this video for grade 8 or 7

I watching this becuase im stuck ratios which understand well

Who’s watching in 2019?

You must get a lot of views during exams

You said -3 * -40 is -120. I thought a negative number times another negative number equaled a positive number

What nice Channel!!!! Thank you for making this channel I'm really learning a lot!

You could even do it this way 5x = 20 is equal to x=20/5 =4

who is watching this and dosen't know anything he is saying just me o ok……

Watch my math class bring down my whole gpa😟

This is pretty good…

bruh my teacher don’t teach

isnt the point confused with a decimal point

multiplication sign

The comment section reminds me why only 33.4% of Americans have a 4-year college degree.

if the x was an n or any variable letter, would it be the same thing? My teacher said yes but what about in algebraic equations?

U u suck👎👎👎

I'm watching this 13 years after this was posted, anyone else?

How many times did my brain go “but why?”

K, how do you convert negative improper fractions in to negative proper fractions?

And why do they “cancel out” and can you clarify exactly what that means?

I am confusion

Won

You are doing the lord's work man. Can't put into words how thankful I am for this.

Can’t be the only one who’s here the night before an exam and want to make sure that they know everything 😂😐

Im bad at school

Maths is used in everyday life

it’s 12:37 A.M., my math finals are tomorrow, and my teacher can’t teach for her life

pls pray that i pass i already have a low C

ṅͤͫ̇ͩͩͣȯͤͫ̇ͩͩͣȯͤͫ̇ͩͩͣḃͤͫ̇ͩͩͣ