Algebra: Linear equations 1 | Linear equations | Algebra I | Khan Academy

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Algebra I on Khan Academy: Algebra is the language through which we describe patterns. Think of it as a shorthand, of sorts. As opposed to having to do something over and over again, algebra gives you a simple way to express that repetitive process. It's also seen as a "gatekeeper" subject. Once you achieve an understanding of algebra, the higher-level math subjects become accessible to you. Without it, it's impossible to move forward. It's used by people with lots of different jobs, like carpentry, engineering, and fashion design. In these tutorials, we'll cover a lot of ground. Some of the topics include linear equations, linear inequalities, linear functions, systems of equations, factoring expressions, quadratic expressions, exponents, functions, and ratios.
About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.
For free. For everyone. Forever. #YouCanLearnAnything
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[@jakelong4510]

Seriously, math teachers need to focus more on clarifying strategies of solving problems rather than doing problems. I still cant find a solid way of solving this bs and i have been looking everywhere.

[@BrainGainzOfficial]

The hard part about that is, not every math topic can be broken down into steps. Clearly the strategy with these problems is to get x on one side by itself, but the way you go about doing that can vary problem to problem. That's why sometimes it's best just to just do a lot of practice problems.

[@jellybarcode.]

@Vansh Makhloga I know math antics it's simple than this

[@vaishnaviravuri3184]

Jake Long Math Antics! Is the solution Try it!

[@bilalmohammed0]

This is a crash course. You need to handle basic lessons on the subject.

[@sneakyninja2281]

ON GOD 💀

[@sayoriutsugj2856]

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

[@loveislife8868]

I am in the same boat

[@PenandPaperScience]

I've just made a new video where I solve several such exercises step-by-step, explaining everything I do. :)

[@Arvinda1x]

@@PenandPaperScience thank you ❤️

[@anouilhdraws3747]

aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa same

[@someone6237]

which grade are you ?

[@noorsar9467]

I am here because my teacher doesn't teach well and she always shout at us if we told her to repeat a single thing

[@neyberto2455]

BlueHarmonizer AROON my teacher don't even explain, she just give the problem and say do it

[@xenecro__4453]

bruh its like you are in my class our math teacher does the same thing

[@shalstynedanathegreat2270]

hey there co harmonizer

[@nasramohamed1867]

Junie Bae wat

[@craftingodst3400]

FACTS AND SHES EMAILING MY DAD SAYING IM NOT DOING WORK WHEN I DONT KNOW HOW TO DO IT

[@mackenziegraves3363]

You explain things better in seven minutes than my teacher does in 2 weeks.

[@richardyoku9979]

if you get it pls help me

[@mrmelons2663]

@@richardyoku9979 u can multiply 10/13 by the reciprocal of -3/4 and then simplify it ik it's been year but i think it would be useful

[@Cam_Oate]

@@mrmelons2663 it helped me, thanks

[@armankalsi4889]

​@@mrmelons2663r ok ll on o

[@nashysworld6938]

Hi yall

[@Corrosiv]

I passed every single class, but math.

[@africanchic1821]

Xander G same

[@AleksGermanSurf]

same

[@calicomint]

I never thought I could relate to something so much

[@killerbean3122]

Math is so easy!

[@olsonbryce777]

@@killerbean3122 ok

[@scratchingdesperado3361]

I wasn’t even a year old when this was posted

[@sbgv8]

same

[@WhyMunch69]

i was just born

[@rene47477]

I was 3 months

[@kaidenknowles2067]

I was -2 years old

[@Moneyshifters191]

I was one day old

[@faithshelley3240]

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

[@ys1r]

people get -smarter- stupider every minute

[@darkmaik6807]

Faith Shelley y

[@darkmaik6807]

Yep

[@dr4g0nb0y4]

I’m watching this 13 years and 6 months after it was posted. Why? I don’t know.

[@jessicacates2002]

i am watching 14 years later

[@adnancharif9296]

This helped me learn an entire math unit in 1 hour after 8 hours of math class. Thank you

[@michaela9914]

This dude's voice is so calming...

[@ezraross5194]

Unlike math teachers at school

[@roshi6]

+ezra luty Watching this at school rn :D

[@RicheyAmigoHerplerGaming]

+ezra luty i swear to god that made my day

[@ChristianRobinson]

+Michaela Terrazas you are gorgeous.

[@NinjaKiwiClash]

+Christian Robinson too much makeup tbh

[@Rightwing789]

One day when i pass school with flying colors and get rich i will donate a large sum of money to khan academy after all there going to be the reason i pass school and become rich . 🙏🏾

[@julli4821]

Actually it makes total sense tbh, not to be a jerk XD

[@shamikagreen5818]

RayZ Bay it does they just used the wrong there

[@LL4MAPAL08ZA]

Horizon_Killa you rich yet bro?

[@tonibuus]

Good luck getting rich with that grammar

[@z_1033]

Meanies all around😑

[@johndragon981]

this dude writing with mouse better than mine with pen...

[@itstheonly7649]

johndragon981 👌🏻😞

[@saahil5790]

Hahaha he uses a touch pad where he connects his pen.

[@jalenbrunsonfan]

Sliite Wyd he moved the mouse without writing so no

[@peacxhtea4130]

He uses a drawing tablet lol

[@mushmins]

I'm gonna fail my SAT tomorrow. Pray for me

[@danielparvin9083]

It is one year later, how was the SAT

[@ololadeoyefeso502]

How was it?

[@flippyj1013]

He failed XD

[@darkmaik6807]

The world Jotaro LOL

[@itstheonly7649]

This is two years later how was it?

[@keeganhutchinson3581]

Wanna hear some bs? My math teacher teaches us nothing at all! First she introduces us the unit we are doing, and then we are given impossible questions to 'make us think', which usually we sit there in silence for 20 minutes. Then she's on her phone doing nothing for the rest of class. We are given 3 days to 'learn' about the unit, and then it's test day. To put this into perspective, the average score is 73%

[@danstewy2452]

I know i'm 3 years late to this comment but 73%? that's amazing compared to my classes average of 50%

[@cyberprinc3ss]

I am internally dying

[@anvikapande7766]

same

[@Coco-xq7zh]

math is fucking killing me

[@DynamicFalafels]

ρυяρlє кιтту same

[@rahanafilsaime594]

ρυяρlє кιтту facts

[@khanacademy]

If you graph these equations, you get a line. So they are linear :)

[@aishaalfalasi9117]

who here in 2020

[@ameeraha1246]

Me aisha

[@VfxArsh]

I wonder if u still reply

[@deathmeter7243]

Hm

[@sampam7231]

Im here

[@cindyds10]

i still dont get it

[@xochiltanielka123]

I keep watching this video over and over and i still dont get it

[@kattyjhonson9323]

yep same over here

[@GumleFunk]

It's Pre-Algebra it's way to easy

[@NWProductionsHD]

Could you be more specific? What don't you understand?

[@xochiltanielka123]

***** thanks that helps alot lol

[@NWProductionsHD]

xochilt m nothings easy on the first go - what you consider impossible now you'll likely laugh at how easy it is next year

[@andreasofia901]

"Have fun" Me: (laughs) ohh I hate math

[@geeshdgk6785]

Same

[@discountpro1030]

It's essential for your future

[@luisgq2358]

i love math ihate gramer

[@dark_matter869]

someone hand me the bleach because I'm officially done

[@ItzBlew]

Dark_Matter

[@ashleysydneylim7098]

Dark_Matter I need a couple glasses

[@kristelleroto]

pass me some of that

[@quixzotic]

Don't forget about me. Sharing is Caring.

[@robertjacob8576]

Dark_Matter hey let me join in the party

[@azile.manqele]

i feel so stupid , maths makes me feel stupid , when my maths teacher walks in i lose my intellect , I get chills , i guess i wasn't destined to pass maths .

[@nikkobird590]

I really don't get math😐

[@Daisy-js9qv]

Math is pretty difficult for me, but you’ll do great! Please don’t feel worried if you can’t understand something, if you feel comfortable ask for help! I’m in 8th grade and algebra is pretty hard for me, although my grade doesn’t matter. You’re doing just fine! Make sure to calm down if you feel nervous!!

[@clashoclan3371]

Hey remember you dont need to be smart to learn math, you just need to be hardworking, I was in that same boat, the smart kids at school would always get an A and they didn't even try at all, I was failing too, but I realized that I should stop procrastinating, I dropped my video games, and studied for hours straight and finnaly got an A, and I understand math pretty well now. Smart people who breeze through their math in school, will struggle in college because they don't know how to study.

[@pabloschaller533]

I think I've said this before, but seriously, were just making life difficult for ourselves with all this math. I mean, look at how well sheep are doing. They're way smarter than us, and it shows. That's only my opinion though. I could be wrong about this.

[@Miloexternalvisions]

If you start young learning the basis of algebra , then your knowledge gets smarter and smarter when devoloping the skills and asking questions. Algebra is very useful.

[@pabloschaller533]

Miloexternalvisions I know, I know, I was just having some fun.

[@Gavin-in2sr]

We’re just getting ready for our future job if you want to become an engineer and your boss says “make me this long of an X and make me this tall of an Y” and it’s just same thing as saving best for last.

[@maryketchum6476]

thanks for refreshing my memory for 8th grade math this helped refresh my memory very well thank you again for helping me out i think your great keep doing what your doing its helping kids like me every were i hope you do well with this product you are great thank you for helping kids like me. p.S. don't stop what your doing never forget that

[@elitegamer7414]

R u in college now?

[@leocabro9745]

I try to understand my math teacher but when I go inside the classroom and the class begins and she starts explaining I have absolutely no idea what she is talking about. It is like she speaks another language.

[@matulin4529]

I hate math but I have to take it no matter what

[@Bored_Peashooter]

Mátû Lìñ no duh

[@zeenatshakil9349]

i can understand same with me

[@DarthTwilight]

I am failing to see the logic behind this. Anyone care to explain why such supposedly unrelated steps are taken to realize the result?

[@lestrangemsp9643]

same 0-0

[@sabahalam6198]

DarthTwilight because math.

[@cadioxavier1632]

Well, It depends on where your from. For example, if you live in the Commonwealth Countries, the Final step after you get the result will have to be simplified. But if your from north america, then you can just leave it at that.

[@cfcfans9758]

DarthTwilight don't worry subscribe to mines I will teach u.

[@myriamefontaine3126]

h we g h ugsys if f cfgdggyfcf Hz shaggyCadio Xavier

[@julienfeliciano9302]

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

[@datgirl8471]

Julien Feliciano 2020🥳

[@toasterbath6997]

For anyone who’s wondering: a linear equation will have two or more variables:)

[@PythonMFD]

@@toasterbath6997 But the equations in this video only had one x. Does that mean they're not linear?

[@toasterbath6997]

@@PythonMFD Hey, I’m not sure how to answer your question so here’s an excerpt from an article: A linear equation is special because: It has one or two variables. No variable in a linear equation is raised to a power greater than 1 or used as the denominator of a fraction.

[@PythonMFD]

@@toasterbath6997 Ah, that actually helped clear things up. Thanks

[@LynnFSTR]

Got through highschool but I forgot it would come back in college

[@rmalik753]

One question how is this gonna get me a job

[@nikkobird590]

Fr

[@zeenatshakil9349]

i know if u grow up and become a doc than where the heck are u going to use pythagorean therom on ur patient

[@rmalik753]

@@zeenatshakil9349 lol

[@zeenatshakil9349]

@@rmalik753 what thats true i spent a whole month teaching myself how to do pythagoraen therom still got a c just tell me which life or death situation will that help in

[@maykaa4000]

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

[@meshcount]

Wow, it's been decades since I've encountered these problems and was surprised I forgot how to solve them recently. I saw your link in the SFGate article and am hooked on re-learning them through your vids. Thanks Mr. Khan!

[@Cypherhex]

meshcount what is your view on math

[@gloriasmith1134]

@@Cypherhex you replied to a 13 year old comment

[@dhoraff]

I am 12 yo and this message 13 yo Damm that's older than me😮😮😞

[@Craftey.]

@@dhoraff lol noob

[@curtisbroderick3182]

Oh the nostalgia of seeing this old technology. But look where it eventually brought his vision. Bravo to Sal! Everything great starts with something humble.

[@omarsulaiman6138]

since the pandemic I've forgotten everything, thank you so much for being such a good teacher

[@simranavaan1140]

I understood all the problems easily :) thank you so much for the video Sir :)

[@adilhossain6674]

Me after watching this:😓😢😦😧😭😭😭😭

[@lizf77]

Thank you for doing fractions! My new teacher only does fractions and its totally new. You're a life saver because I got a quiz tomorrow on this stuff

[@randomtheory4805]

"That's a big fat five" Me: That's what she said.

[@imogen9427]

164 people gave up on liner equations. i gave up a long time ago...

[@shaheertariq1116]

Imogen me too I give up

[@pizzapizzapizzadonut6299]

Imogen you probably gave up on english too because you can’t spell linear.

[@irumnazar6470]

fazoul😒😒😒

[@c0ntra605]

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

[@qxwlytt]

I wish I could pause and rewind my teacher like a video

[@youmadiakite2007]

thanks you dont know how much you've helped me! i was freaking out about a test that i have tommorrow but now im at ease . thank you

[@lilsuki5941]

This was posted 1 month after I was born 😂 I'm now 13 years old

[@ameeraha1246]

I'm 13 too

[@hibrix7408]

@@ameeraha1246 I'm also 13

[@ameeraha1246]

I'm actually a boy I'm just using my mum's account.

[@ameeraha1246]

Like my mum's phone

[@jonesthegreat9711]

Same

[@haider1905]

I appreciate your effort but instead of teaching the rules and methods. You have just solved the question without telling what rule to use.

[@cory8242]

need to go back to the arithmetic videos

[@weeFred]

I really wish Khan Academy was around when I was at school!

[@barbosaif]

Man, What a wonderful thing that I found you here. I am from South America and am preparing myself to get the Gmat. You are so smart and are helping me a lot to improuve my score. Thanks a lot.

[@dontmindme.imjustafraidofe9327]

Watching this to help me go to sleep at night! Hope it works! *22-hour later EDIT:* Well, I did end up going right to sleep and was so confused as to why my phone screen was on. Hopefully it’ll happen again!

[@westsidecartel90]

thanks now i feel confident that im gonna pass my test

[@Dulex123]

How you do?

[@westsidecartel90]

@@Dulex123 Lol have you noticed how old is my post and video cant even remember

[@Dulex123]

@@westsidecartel90 how old were you when you made this comment?

[@chaneld152]

Love the way you explained this. Thanks!

[@joseph4756]

The point is that, in many situations in life, you will have some amount of information, but not all of it. This is a technique whereby you may be able to confidently, logically fill in the gaps, thereby having full information with which to proceed in whatever it is you may be doing. This is extremely useful in many, many, many situations!

[@Kimi99]

your my hero!!!! thank you so much for putting all of these vidios on youtube, they're great!!!!

[@danielparvin9083]

Kimi99 geuss what! You saw this guy before he made a website, HQ and became famous!

[@theredninja2953]

2007

[@Gkze22222]

@@theredninja2953 nov 2006

[@dhoraff]

I am 12yo and this comment is 15 yo 3 years elder damm

[@jjc.shelby2177]

Sit the fucc down school, let this man stand.

[@clashoclan3371]

School is way better for learning(if you have a good teacher), khan academy is just there to complement it.

[@IQ-rl2wx]

Understanding the basics of math, is really importent as it forms the basis for other fields

[@radams103]

I love the way, you explained it and showed example of different equations.

[@kemydeschampsdeschamps524]

Wait a minute...don't you change the sign when you make a reciprocal? I'm confused

[@learnwithpi]

Nope! The reciprocal of a number is something that when you multiply the original number you get 1 ! For example, 2/3 x 3/2 = 6/6 = 1 or -2/3 x -3/2 = 6/6 = 1 If you changed the sign you would be multiplying a negative by a positive and you would end up with -1. We want to get a positive 1. So if our original # is negative, our reciprocal will also be negative. Because negative x negative = positive :)

[@hinarizvi8496]

Are you really happy to make this world a better place please please reply I will wait

[@nadaaltalawy5370]

Guess you waited for a very long time, huh?

[@nisargpatel3390]

Still waiting or given up?

[@theyoyoman103]

Still waiting

[@Angell77777]

Hina Rizvi still waiting?

[@illuminatislayer6340]

Hina Rizvi still waiting

[@scarecrow763]

This video is very useful and it helps students in high school and college. It not only helps students, it boosts their learning skills and helps them solve real world Algebra math problem. Thank you so much Khan Academy for helping students learn better in math! 😎😎

[@vishrutkinikar2311]

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

[@PenandPaperScience]

For those that want more practice, I uploaded a video where I solve such exercises step-by-step, explaining everything I do along the way for minimal confusing :D It might help some of you out there :}

[@N0XKlA]

where

[@N0XKlA]

i cant find it

[@N0XKlA]

please

[@joshhend6718]

Thanks for the help !

[@KhalilShqair]

your the best... I'm done school long time ago... but your videos are a good way to refresh my math...

[@johnrobinson518]

Awesome! I really enjoy the way you explain things. Thank You. J.R.

[@teawithzonroxbleach9433]

this save me from failing my exam tomorrow 😂

[@BossChronicles]

MATH 10 Introduction to Statistical Reasoning OR PSYC 10 Statistical Methods in the Behavioral Sciences I'm not good at math and want to take the least difficult course which would be easier between these two?

[@OuttaEgypt]

You're like my shiny, golden, math Messiah or something. Thank you so much for making things so simple!

[@mrplatypus333]

Thank you so much!!!I was skipped from seventh grade math to algebra 1.You helped me alot

[@jiroatencio9005]

don't let your self get tired chose the shortcut

[@moajunglajamir8781]

these comments are so old its scary

[@sufy3612]

This is helping me a lot i’d recommend this channel because it grows peoples brains

[@yvettesrogers119]

Thank you for ALL the math tutorials, I made A’s in all my college courses! That was in 2020-2021. I was able to obtain a Bachelors degree, Thankyou!

[@akashmishra5424]

Contact me. I am indian. and you

[@bryiannamorris]

who created algebra and why it’s literally irrelevant to everyday life.

[@martenmina1346]

ikr

[@mightykraken1998]

But algebra is one of the most important subjects to learn

[@bryiannamorris]

@@mightykraken1998 its a bunch of nunbers mixed with the alphabet what job requires that?

[@mightykraken1998]

@@bryiannamorris Well, I don't know . Maybe mathematicians or math teachers. Other than that, I'm clueless.

[@mightykraken1998]

It's funny too on how I'm doing my algebra homework now. Lol 😂

[@nandoreive]

very good' sou aqui do brasil e aprendi direitinho do jeito q vc ensinou ! Valeu obrigado '

[@StriveForExcellence2]

A great tutorial, thanks!

[@mariekamara5078]

Thanks i understand now. And u teach very good, keep it up.

[@BoarPit]

I have all A's except for math which I have a F in

[@sadbunny_69]

thank you so much for this, its very helpful, i suck at math period!! you explain very well ,

[@pierceamedi8260]

You wrote this 12 years ago, you doing good?

[@sadbunny_69]

@@pierceamedi8260 no. I’m dead now

[@pierceamedi8260]

@@sadbunny_69 hows being died

[@sadbunny_69]

@@pierceamedi8260 nice and peaceful, how’s being alive?

[@Dulex123]

How old were u when you made this comment

[@examtoppers7541]

this was really great way of solving these problems....thank u... and is anybody watching this video with me in (may 2021) bro get it these are really very important questions.

[@NexGenRebirth]

i am young and want to make sure i can have a good grasp on most things so that when im older i can just pluck this out of my mind and use it. you make this really easy sal. thank you.

[@ivkaransawhney5576]

To Android Users: Download "MathChat" (A new chat enabled application) to get help on any math related topic and help others anytime!! CHEERS!! GOOD LUCK!

[@davidsong_toomad]

Anyone 2019?

[@spongebob1619]

This vid was made 12 years ago

[@ameeraha1246]

2020 boiii

[@user-sr6ir2vu1y]

you made it so easy to under stand !!,... thank you

[@guapdaddy7338]

This lesson is older than me but it’s still saving me

[@BilalAli-rh2cx]

I wasn’t even born when this was posted

[@roni6752]

I watch this video for the asmr

[@DACsAcademyOfMath]

Sal you and Vihart inspired me to begin making educational videos , thank you so much. I also have to thank John Stossel who made a story on a news channel which mentioned your work. thank you again Sl.

[@anna-bs6wv]

thank you. u jogged my brain a lil, its been a long summer

[@chime6454]

I'm just here cause I missed my teacher's online class

[@mohaalrashedi3181]

CaNt rEaLaTe

[@YasminsEatery]

No offence but there is a simpler method for the 1st one...x=20/5 .....because 5was in multiplication... So if it comes to other side the sign will change to division....

[@tradergirljam]

Let him teach

[@YasminsEatery]

@@tradergirljam when did i tell him not to?

[@fat1t1]

THANK YOU SOOO MUCH!!!! THIS VIDEO HELPED ME A LOT, I'VE BEEN SUFFERING FOR SO LONG ON THIS LESSON :'( THANK YOUUU!!!! :D

[@mihaeladog7187]

I can’t thank you enough, I do contribute but that’s just a small toll of appreciation, close yo nothing compared with the benefits I get.Math is not easy for everybody , your lessons are so easy .

[@haknumanMC]

Hella easy

[@shxx_x]

Who’s watching in 2019?

[@Dulex123]

2023?

[@Yomi-san]

Great video, very easy to follow

[@animalvidsforyou]

Very well explained I always use 6x=24 for an example. Divide 6 and 6 which is out then divide 6 into 24, which is 4, x=4.

[@qeyanzar]

Watching 2019

[@diamonddisciple8751]

who watching in 2017

[@LightningBoyNation]

meeeeee

[@H4m0ody]

@jesse aparicio godamn

[@jakehupp5864]

Algebra is hard as hell when my teachers explain it but when khan does it its awesome

[@Seattle206723]

5:45 in the video, why didn't he just cross multiply both and come up with 10/13? Just a question I love Sal's videos. He helped me get a 3.7 in math this quarter. Thanks Sal.

[@why712]

This was 10 years ago

[@bnuggg]

TAYLORRRR pleasure to see you here

[@neyberto2455]

why712-asmr darlings personal account 12

[@Dulex123]

This was 6 years ago

[@why712]

@@Dulex123 ahh yes, highschool days

[@oliviervalentijnderuyter974]

So at 5:55: Why is X -21over20 and not -42over35? Why does -6 change into -3 and 8 into 4? Do you only do this when these numbers can both be devided with the same number?

[@jellie1443]

1. When you multiply fractions, you multiply the numerator and denominator then simplify. 7 x -6 = -42 8 x 5 = 40 -42/40 = 2(-21)/2(20) cancel the common factor which is 2 and you get -21/20. 2. It's called cancellation wherein you cancel common factors. -6 = 2(-3), 8=2(4) 2 is a common factor, so it's cancelled.

[@Av3rag3jo3zzz]

you should be a teacher, thats the first time I've ever heard anyone explain simplifying so well, anyways will there ever come a time when you dont do cancellation?

[@oliviervalentijnderuyter974]

+Jela May Yap Thanks for your reply!

[@jellie1443]

Joe Davis You don't do cancellation when the numerator and denominator DON'T have common factors

[@kkboi7753]

oh thank you! your explanation is so essay to understand.

[@tie7626]

this video is now older than most of the people learning from it