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

[@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..

[@sarius2388]

@@pythkro why bother typing then? Extra effort when you're trying to not exert any. @RoyalSpaceship I wholeheartedly agree with you, I like it when the teacher explains every step without assuming we have pre-existing knowledge, whereas sometimes they skip too much of the working and it can confuse us.

[@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

[@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 Curriculum is obsolete at this point...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

[@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

[@avemunsayac]

@colloredbrothers Thank you for inspiring me and I'm 15 years old and Wish me good luck I'm trying to get to the calculus level.

[@astrozombiez1]

did you ever make it to the calculus level?

[@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

[@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!

[@sankalp7135]

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

[@omarct]

Thxs bro, this totally helped me out, I was stuck on 2/y+3 + 3/y-4 = 5/y+6 , but when i saw 5:00 I understood what i was doing wrong, it was the way i was multiplying it. Was doing 2(y-4)(y+6)= 2y-8(y+6) , instead of 2(y-4)(y+6)=(2y-8)(y+6). You overlook the simple things sometimes.

[@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.

[@7ramonagrl]

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

[@mycosartorius9064]

**SEVERELY SHOOK**

[@aanyamehra1621]

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

[@charcain1123]

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

[@colloredbrothers]

Seriously this is fucking magic, maybe it's because im older and i have a clearer mind but this seems so clear to me now, it's so obvious. I have always been a bad math student I could never understand it and suddenly now its so easy. My whole college direction was consciously chosen to avoid math in any sense because of my giant ignorance in the field and here I'm learning it with ease. I swear If i had this 6-7 years ago it would totaly change who i am today and what I do.

[@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 :(

[@templar19]

Very nice. I'm a math tutor myself, and this is a great way to break such problems down for weaker students. One critique: you omitted the check for non-permissable values.

[@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,

[@vicksoma]

@erule92 'x' is on the dividing side of the fraction...so he multiplied it by x to cancel it out. It cancels out because anytime you divide and multiply something by the same thing (in this case x)...you get 1 (which when multiplied or divided keeps the number the same). So like if you have the fraction 4/5 and you times it by 5...the 5's cancel out and you get 4/1 which is 4. He wanted to cancel it out because having x in the denominator is useless to solving the problem. It needs to be alone.

[@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 :>

[@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.

[@anumehaxo07]

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

[@Seattle206723]

The first equation, was that a linear equation? If so im going to transfer out my class. The teacher I have seems to think those type of equations aren't linear. I trust in Sal he's the man and I would expect his title of linear is correct.

[@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.

[@Lilandriel]

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

[@yobropro5696]

He is very good

[@gamingwithkevin7344]

like u

[@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?

[@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.

[@YeetusEliteus]

i skipped year 8 and am in y9 this year XD.. and still top of the class in advanced maths, science, english, P.E, and music :P

[@astrochemistry3867]

u prob almost out of college now!!! that's crazy im doing honors 8th grade lookin at this lol

[@NatePlaysGamesALOT]

@@astrochemistry3867and your probably almost in 12th grade now!

[@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

[@KAYDENSAINTS]

im in 5th grade and i study algebra by my own! >w

[@edgarsanchez3838]

Carly Santos nice man this shit gets hard when it hits you in 8th grade

[@tompodgorelec9859]

Same I year 5too

[@mattholt7855]

lol lil kids

[@scrumptiousdumpalings5322]

Carly Santos same dude! Or girl, idk

[@fivenightsatlospollosherma5893]

Me too!

[@BSkwizzle95]

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

[@shreyasgode6962]

Awesome I improved my math skills

[@joevjohn6265]

thank you im in pre algebra and im trying to get ahead in algebra 2, this is going to help me at a math competition at Gannon university.

[@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.

[@VASEA0000]

well if you have 3/x+5=8/x+2 you can easily do it with a simple method >>>> 3times(x+2)=8times(x+5) >>>> 3x+6=8x+40 >>>> 3x-8x=40-6 >>>> -5x=34 >>>> x=-34/5 >>>> I don' t know what's the name of this method but it's working great for me you can test it for yourself . Too bad i am at philology!!!

[@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

[@Onap3]

You make math so FUN!

[@jhonsmithers4853]

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

[@Vman6744]

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

[@HalfkastHybrid]

You are a champion. Needed a quick refresher course for linear equations for an upcoming test. Couldn't find (x+a)/(x+b)=c anywhere else online.

[@Tekrow]

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

[@KhadeejaMansour]

thank youu! 17 years old and 17 yrs later

[@shannenlibres2365]

When I heard his voice I just thought "his voice sounds younger like way younger" then I check the upload date and holy schmoly this was 14 years ago

[@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

[@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

[@magicdude21]

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

[@thebillybobhobillybo]

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

[@sivakumarmodha6609]

its good teaching. thank you khan.

[@ImmortalDragon]

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

[@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

[@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.

[@rohitgoyal2089]

Good

[@alexia942]

All of your videos are very informative and helpful. Thank you for taking the time to do them.

[@fazalhussain985]

thanks khan academy

[@kshitijprasad4402]

this video is awesome. it helped me in algebra

[@hiccuping621]

Im learning this in GRADE 5 in Australia

[@deleted9347]

9th grade algebra or 5th grade algebra?

[@letsvision5589]

Level 4 is hard than I thought

[@HoneyPup-my9gk]

THANK YOU

[@SuperIm1234]

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

[@IandYou0]

Algebra is hell, lol.. But i like a challenge..

[@chloeherrington2022]

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

[@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?

[@chuly413]

3:34

[@lazaro802]

I know this is old but even if its 10 years ago THIS IS BETTER THAN WHAT MY 8TH GRADE ALGEBRA HONORS 1 MATH TEACHER EXPLAINS TO ME I LEARNED SOO MUCH XD

[@1873Winchester]

After looking and looking I think I get it now, but using fractions makes this a nightmare. I am not american and fractions where gone over little in school and never used in real life. I do love decimals.

[@unknownz1238]

This is life saver Thank you

[@emilyplays159]

Thanks sir

[@DanielGarcia-fh6ij]

thank you for all of the things you showed me

[@SilveraLordz]

@Lilandriel one over one (or 1/1) is the equivalent of 2/2 they both reduce to equal one (because one divided by one is one and two divided by two is one) He just wrote it as a fraction because while working with other fractions it makes it easier to compare the two, thus he could've used 2/2 also but 1/1 is easier to use ^~^ hopes that this helps

[@bennettmalcolm3943]

actually really helpful 😊😊

[@KickAssManist]

were did the one-fifth come from

[@GQ-jv9uw]

KickAssManist same? I have

[@foreversleepy4379]

Because 1/5 is the same as saying 1 divided by 5, and what is 1 divided by 5 in decimal format? It's 0.2, which is another way of writing 1/5. Now, because we wanted x on its own, if we multiply 0.2 by 5, what do we get? Yup, 1 whole. and 1x is the same as x, therefore, eliminating the 5 out of the equation and leaving us with just x.

[@karimwaziri791]

very happy to see your incredible tutorials

[@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

[@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

[@Subzerotn]

yes thank you! your vids are a wesome

[@dianawestrup7416]

Very helpful! Thanks!

[@souleben]

Either 24 or 25

[@billydakid3]

you teach better then my teacher :O

[@123vdogg]

thanks so much!

[@fazalhussain985]

really i learned more in 7 and half minutes

[@titanrifle4321]

this is sal when he is sick

[@PhantomLyric]

I know algebra and this is just a review for me so I can move on to calculus, etc. However, I found the wording on this video confusing. You said "minus 6" instead of "negative 6" - The terms can be confusing because you use "minus" when referring to the operation. Don't get me wrong, I think you're a god among men for these videos because they are really great! I just found myself confused on this particular video.

[@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.

[@minivanjack]

It was not explained how "7(x+1)" turned into "7x+7" .( we don't know what "the distributive property" means). Please explain.

[@ColdPenguin6297]

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

[@SilveraLordz]

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

[@Richard133t]

Okay I got a question how do you know which side to subtract from? Lets say i've got 6x+6=15x+30. Should i minus 6x and add to 15x or minus 15x and add to 6x and why?

[@chrissatterly7071]

I was wondering the very same thing. He lost me when he did x+2=7x+7. Why did he subtract the 7x?

[@gotouguts2066]

@@chrissatterly7071 It doesn't matter, it's personal preference. You can just as easily subtract the x on the left side from the 7x on the right and you will still wind up with the same answer. He wanted the x on the left because he always likes the variables on the left- I simply do what I think is quickest.

[@gotouguts2066]

@@chrissatterly7071 So in this example, you could subtract the x on the left from the 7x on the right and you will still get the same answer. The important thing to remember in an equation is that what you do to one side, you have to do to the other side.

[@AztroCreationz]

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

[@jodinha4225]

AztroCreationz dividing by one isn’t needed to begin with

[@Debedeb]

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

[@savitrijonnalagadda7045]

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

[@kdmq]

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

[@Supreme0757]

thx

[@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

[@colloredbrothers]

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

[@DarthGnomian]

all he is really saying is divide it by 5, you don't have to use it as a fraction, its a little more complicated that way, dividing by 5 is much more simple

[@JEFFCLEVANDR]

Is there a list to show what the next lesson in line that would come after this... What lesson would normally follow if you were to take this in school... I am trying to find it but I don't see anywhere that shows it???

[@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.

[@jamundi308]

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

[@platelet8695]

I kinda learned something...

[@vkain100]

Love your videos Sal, you're helping me so much i feel like i should pay you. :)

[@beasterjames131]

X=15

[@beasterjames131]

+Beaster James four the first equason