Algebra: Linear equations 4 | Linear equations | Algebra I | Khan Academy

Courses on Khan Academy are always 100% free. Start practicing-and saving your progress-now:
www.khanacadem...
Solving linear equations with variable expressions in the denominators of fractions
Watch the next lesson: www.khanacadem...
Missed the previous lesson?
www.khanacadem...
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
Subscribe to Khan Academy’s Algebra channel:
/ channel
Subscribe to Khan Academy: www.youtube.co...

[@RoyalSpaceship]

Contrary to what other commenters say, I believe your videos to be incredibly in depth and very helpful, especially for review when studying Calculus! You don't take any shortcuts, making the process so much more understandable. Thank you!

[@pythkro]

Brent Henry I wasn’t even bothered to read what you said, although (I think) you make a fair point..

[@dhruvs8139]

Lol, I learned more in 7 and a half minutes than I learned from my teachers in a week.

[@fivenightsatlospollosherma5893]

lmoa

[@MetaphysicalAxiom]

and the downfall of curriculum is observed in the inefficiency compared to the dark web intellectual curiosity based approach. Curriculum is obsolete at this point... or actually going to school is so wasteful at a societal level. Access to to knowledge is really all we need most of the time.

[@zeyadessam4173]

true asf

[@keegankattler2774]

Dhruv S, sane

[@keegankattler2774]

Same

[@rawrpowerx]

i'm homeschooled. and i watch your video's almost everyday just to help me out a bit since i basically have to teach myself. i would literally pay for your tutorials, man. :D

[@ilovyongbok]

I was having such a hard time in algebra but this made me have an easier time in algebra, thanks for making this video

[@sankalp7135]

i always do by an easy method its"cross multiplication"

[@urielxicohtencatl1887]

dang he explains it kinda better than my teacher

[@libriumdev]

Ikr now instead of getting a 97 on tests in getting perfect scores.

[@2kmichaeljordan438]

I’ve basically been teaching myself math with mathpapa, khan and mcbrian since I started high school

[@charcain1123]

Dividing by 5 was easier for me -very well explained-thank you

[@Nadrealis]

@waaathaaa Since the x+5 is in the denominator you have to MULTIPLY to get it out of it's place as a divisor. If you think about it, Multiplication and Division are merely the opposite of each other. Yin and yang. The same is true for Addition and Subtraction. So to get something out of a divisor placement you must multiply it. To get something out of a quotient placement you must divide! I hope that helps!

[@jela-yah1202]

Thank you so much. Your 7 minute videos helped me comprehend more on the lesson rather than my teacher's 1 hour long lessons :>

[@paigemadeline4320]

I've been teaching myself algebra on this playlist for when I go to the next grade to have an easier time.

[@gokurocks9]

Keep going, you'll look phenomenal to all of your teachers

[@nocturnalvisionmusic]

+ Just Paige Where did you get your profile pic from?😃 It's adorable 😊

[@nocturnalvisionmusic]

Aww cute pic is gone now :(

[@7ramonagrl]

aww listen to baby sal :) over 10 years ago!

[@mycosartorius9064]

**SEVERELY SHOOK**

[@aanyamehra1621]

Almost 13 years...That’s how old I am-

[@BSkwizzle95]

From the first level to this last one were so easy to follow. Thanks so much.

[@Lilandriel]

@SilveraLordz actually, I think that does help! thanks for taking the time to explain :) much appreciated

[@slatha1556]

Khan academy is a simple way to learn maths very well. We can easily understand the topics. This is the key for maths. We can easily solve difficult problems in a minute when we see this videos. They will say in a simple and easy methods.

[@wh7227]

Sorry, but I'm a little unsure about that first problem. How does 5=3 fifths? Also, on the second problem, when you minus 7x to 7x +7, then on the other side it's + X why is that? I understand why it ends up as -6. Just not why it wouldn't be -8.

[@chrisusedtobetheman8.079]

Me top at 4:30 , why was it multiply by -1/6? And not just divided by -6... As for your question, he chose to move everything to the right which got him to that point. Usually I'd move everything to the left which gets you a different answer.

[@Tekrow]

I also need help with (7/x+4)-(5/x-4)=(12/x to the 2nd power...-16)

[@rj2k1]

Solving linear equations with variable expressions in the denominators of fractions........the description alone will frighten the weak of hearts......that being said ill keep on watching till it get into my system.

[@flower4536]

thanks so much this saved my life since i got in my algebra class almost an entire month into the new school year i had some catching up to do and this helped me alot

[@SalmanAli-wq9yt]

bro are you still alive?

[@Thannisan]

Like many others have expressed, I wish you had been there instead of the indistinct mumbling, arcane rules, and back of the head I was provided with in my introduction to Algebra,

[@amadorivanc.3645]

Thx khan academy this helps me a lot because this shows all my modules and topics I need in my Grade 8 mathematics thx so much pls send more videos of math

[@chloeherrington2022]

I love how this was posted the year I was born 😂

[@yobropro5696]

He is very good

[@gamingwithkevin7344]

like u

[@Sukuun]

These aren't linear equations; they're rational equations.

[@leonardocuritiba1]

Thank you, you're right, of course. I didn't know that and when I searched to confirm, "Bazinga"!

[@ti84satact12]

You're correct, but he's showing how to transform them into linear equations.

[@theevangelistchioma]

Net Neutrality so true rational equations

[@1873Winchester]

I feel as if this video jumped over several explanative steps as the earlier videos did. I don't understand how and why the equation works. Seems to me that this is more for refreshing rather than a learning from the ground up video. I have no previous experience with math like this. The earlier videos explained every step though and made it easy to understand.

[@shreyasgode6962]

Awesome I improved my math skills

[@HerZong]

Thanks for showing this video in KZbin, study in here or your video is much better than in college. And very easy to follow, wich step I don't understand I can just reviwe it. Again than you very much.

[@jhonsmithers4853]

I struggled for a month in this unit and sal khan taught me it in 7 minutes.

[@janice7832]

I haven't been to school in more than 40 years. I've never needed algebra and don't know why I have to learn it for my GED but I do. Maybe if I knew WHY we need to figure out what x equals. Are we cutting wood? Are we rationing food? Are we measuring rectangles?

[@CaptainZhariff]

i dont care whether i do use math in my future or not but i do love doing math and i will always learning non stop even though if i know its useless

[@JonLG490]

+CaptainZhariff even though if you know it's useless? smh

[@janice7832]

Thank you jvwIdeAwake

[@naimbey7824]

+Janice Mills Math is intended to measure the universe like the ancient Asiatics did

[@jomuni]

+CaptainZhariff same here

[@TunezCottage]

I didn't get -34/5 I only got 34/5 because instead of getting rid of the 8x I got rid of the 3x first, and my result ended up different, how do I know whether or not I did it right because you should be able to do it either way.

[@user-kp5kg5dl8h]

TunezCottage it should still be negative either way. Subtract 40 from 6 and then divide by 5, right?

[@NazHasanHuda]

Either way, it's negative. If in doubt about the answer, check at desmos dot com/ calculator: www.desmos.com/calculator

[@sentrasersr20de]

what is the precursor to Algebra that I must understand before learning Algebra?

[@titanrifle4321]

this is sal when he is sick

[@sivakumarmodha6609]

its good teaching. thank you khan.

[@samayoa95]

On the 3rd step: Why choose to take minus 7X from the left side? Couldn't you choose to just munus 1X from the rightside?

[@lestrangemsp9643]

what if u wanna get the answer to decimal point like instead of times1/5 devide by 5 is there a way to do that without a calculator like a fast easy way

[@tugger]

why would you work decimals without a calculator ?

[@me3thestar7]

I just love it how he makes it awesomely easy and then he's like "let's do another one" :D

[@ahard-daysnight6659]

agreed, 9 year old comment

[@me3thestar7]

@@ahard-daysnight6659 lmao thanks for that kick of nostalgia

[@ahard-daysnight6659]

@@me3thestar7 yeah np :D

[@SalmanAli-wq9yt]

Remeber@@me3thestar7

[@TheNClegend96]

on 4:53 can you cross multiply or will that not work there?

[@Onap3]

You make math so FUN!

[@anumehaxo07]

this is soo much more complicated than it needs to be.......

[@clayharrell5682]

This makes sense, but I'm a little hung up on this problem 3x(x-1)=18 How would this work?

[@adityaguin4913]

You would distribute the 3x(x-1) to get 3x^2-3x=18. Then subtract 18 from both sides to get 3x^2-3x-18=0. Divide by 3 on both sides to get x^2-x-6=0. Now what two numbers multiply to make -6 and add up to -1? It's -3 and +2. Thus (x-3)(x+2). Since one of them has to equal 0, your solutions are 3 and -2

[@tumbleweed8797]

x=7

[@jasanpahaf]

4:41 & 4:48 => that's what happens when people think too hard about something... they tend to forget the other little details. when taking tests, don't forget to breath and fulfill your brain with enough oxygen.

[@rohitgoyal2089]

Good

[@Vman6744]

@Chequelito14 it works either way he did that because he didnt want to end up with a -34 on one side

[@Alefevre101]

1/5 part is confusing please reply.!! I need help.

[@liamfenton3287]

ok

[@pringlets]

8 years ago

[@Ginatron]

From what I understadn, you subtract the number that is furthest away from x, so since 7 would be the furthest number, that is the number that you should subtract. I'm pretty sure that's it, but you might want to talk to your math teacher about it.

[@vicksoma]

@EnemyBikeCo He didnt square x. Since it was in the denominator (the dividing side of the fraction) he multiplied it by x. And did the same to the other side of the equals sign to keep it equal. If you divide and multiply by the same number they cancel each other out and make 1. It's like adding and subtracting the same number gives you 0. In this case it was divided by x...so he multiplied by x to cancel it and make it 1 (and anything multiplied or divided by 1 stays the same) so he got 3.

[@SalmanAli-wq9yt]

real

[@DanielGarcia-fh6ij]

thank you for all of the things you showed me

[@unknownz1238]

This is life saver Thank you

[@badgotohell]

Shouldn't the added x be -x to be able to cancel-out the +x

[@scarletswaine7132]

is there a video teaching level one gradients and intercepts in algebra?

[@ShaneMPell]

Can someone please guide me through solving 3x-2/2x+3=4x+4/2x-2? Or any other equation that has the variable in both the numerator and denominator?

[@Onap3]

@Richard133t IT can go either way, but I suggest you do 6x-6x+6=15x-6x+30, because this way your coefficient wont be negative if. My teacher told me to subtract the variable to the number with the largest variable (Sorry if that was confusing, what I'm saying is, since 15x is bigger than 6x you would "get rid" of 6x). Hope this helps you :D

[@SalmanAli-wq9yt]

i agree 11 year old comment

[@Debedeb]

would be perfect if ; you were to show every step made including reducing etc

[@Subzerotn]

yes thank you! your vids are a wesome

[@dianawestrup7416]

Very helpful! Thanks!

[@nikitoe7214]

In the last question in the second to last step why did 8x become negative

[@jooalee6440]

What's up with the quality?

[@HoneyPup-my9gk]

THANK YOU

[@Lilandriel]

can someone explain why he's used x+1/1? i get the x+1 bit, but why the 1? why not x+1/2? or even 3? one of the reasons maths throws me is that i just don't get that sort of arbitrary decision, and it's really frustrating

[@AztroCreationz]

The 1 Under the x+1 wasn't actually needed, right?

[@jodinha4225]

AztroCreationz dividing by one isn’t needed to begin with

[@hiccuping621]

Im learning this in GRADE 5 in Australia

[@deleted9347]

9th grade algebra or 5th grade algebra?

[@ligener]

how can you check a fraction over a fraction

[@renasania1336]

2:20 why the parenthesis around (X+1) ?

[@norm98]

thank you so much !

[@ImmortalDragon]

@Dagangstapapi 3(x+2) = 8(x+5) 3x+6=8x + 40 < you multiply 8 by 5 which equals 40

[@emilyplays159]

Thanks sir

[@SilveraLordz]

@Lilandriel Welcome ^~^ I'm glad it helped :D

[@skyapproved7148]

I thought a line and then a thing underneath was a fraction or dividing why are you saying multiplied by in 5:00?

[@colloredbrothers]

@13sophiecat 8over x+2 not 12. I'm geussing thats why the outcome doesn't seem logical.

[@alexalexisalexy]

Can someone explain why you times by 1/5th? That's never explained where that 1/5th comes from.

[@quackjcj12.32]

What if the x is in the numerator

[@siddharth-wy2kp]

u cancel the denominators

[@SuperIm1234]

I'm in year 10 now! I second in Maths and English!!

[@professoresteve90]

is the answer 6.5? when you divide it by 5?

[@thebillybobhobillybo]

guys he multiplied by 1/5 to get 1/5x5/1 which cancels out to make 1x which is x.

[@skandhable]

what program did u use?

[@magicdude21]

for the first part ofthe vid: just say multiply by the recipricol thats easier

[@troublesome07]

As soon as fractions are involved I have no idea what's going on

[@Blackreaper95]

Why does the 5 turn negative?

[@letsvision5589]

Level 4 is hard than I thought

[@smallsycoraz514]

thanks

[@arnoldaji4042]

why cant u multiply both sides by 1/3 for the first question?

[@billydakid3]

you teach better then my teacher :O

[@ChildHoodHorror]

@ChildHoodHorror Nvm he explains where i got lost on the next line

[@EnemyBikeCo]

0:40 Wait, why would squaring "X" make it cancel itself out?

[@aanyamehra1621]

Lol I know I’m suuuuuuper late, but It’s not being squared, it’s being multiplied... so the X’s in X into 3/X would cancel out, wouldn’t they? Edit: that doesn’t quite make sense but write it down in a notebook or somewhere, you’ll see yourself

[@lunarcloud5827]

For the third problem, I’m pretty sure thats wrong. Aren’t you supposed to subtract or add the lesser number with the other number to solve? And you didn’t combine like terms on each side of the equation, i’m overall confused.

[@kdmq]

If you cross multiply the last problem, it'll save you lots of trouble.

[@savitrijonnalagadda7045]

Me as a fourth grader learning lots of math and don’t know distributive property

[@OneHellofaMind]

I personally dont like how he does the times 1/5. I would just divide by 5, its a lot easier. And when he's try to cancel out one of the x's on one side he always subtracts the bigger number and thats a lot more confusing and harder to me. If I had 3x and 8x I wouldnt subtract 8x, that just makes the equation more complicated.

[@crumcon]

Could anyone explains how -1/6 x -6X = X ?? on the last two line. ( 04:29 )

[@mrmagus4553]

It's really confusing when he words it like that. What he actually means is that you divide 6x by 6 to get x by itself. It's much easier to do it that way in my opinion.

[@fazalhussain985]

really i learned more in 7 and half minutes

[@maths9015]

how do x cancel out?

[@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!

[@souleben]

Either 24 or 25

[@ekpsych960]

So if X = 3/5, then the original fraction was 3/3/5?

[@ColdPenguin6297]

@ChildHoodHorror Distributive Property. 8 times x = 8x 8 times 5 = 40

[@jamundi308]

I crossed multipled.. its easier and less steps. =)

[@Mortis33-o4b]

isn't using fractions more complicated?

[@andrewvaughan5163]

this video is not as good as the rest

[@AryanaSreshthaReede]

It's a video from 2006!

[@MetaphysicalAxiom]

I thought the same thing but it really doesn't matter. It's clear enough... doesn't have to be pretty.

[@kolson13069]

why don't you teach them cross factorization much simpler???

[@DimondAtlas]

omg seems so easy now :D

[@ilovecharlie123451]

do u have level 6?