Introduction to solving an equation with variables on both sides | Algebra I | Khan Academy

[@MODAV]

An 8 min video, it took my teacher a whole period to explain this

[@numbersletters2920]

1➗85=

[@AstralGarden101]

Mo 193 teachers take too long

[@homeboi808]

As a teacher, we are “forced” to teach from bell-to-bell, so even if I know it’ll only take 20min, I have to stretch it to ~1hr because my bosses think that is better.

[@symbolbouchardnoteira8155]

@@homeboi808 math is infinite and eternal life is finite and our limited life span is too short at present explain it as fast as possible because I am certain in modern era a lot of people want desire a higher education.

[@antinoye973]

Mo 193 my teacher doesn’t even teach ... LITERALLY... she gives us videos that don’t really help..

[@summerglitter1831]

dear algebra, dont ask me to find your x, she is not coming back and dont ask me y

[@carolinerose7511]

summer glitter I LOVE THIS COMMENT 😂💕

[@mayawildes2818]

dear math, I am not a therapist- solve your own problems

[@grannie5957]

summer glitter lel

[@laibakhan2261]

Cliche

[@vincenttheodorearifin7305]

Hahahah

[@brendajones5186]

Thank u, my teacher doesnt know what shes doing im get in now

[@nova-rd9in]

Lol

[@Ethan-qe8pe]

Same

[@twerkonlilbro]

Lmaoo

[@imakevideos5186]

Same

[@Logan-ct5sm]

Same

[@dragen147]

thank you my teacher does not understand that no one understands what she is doing.

[@suruchichaudhary606]

@Alexia Aflallo Álvarez de Toledo what do u mean?

[@numbersletters2920]

1➗82=

[@kamto_fine555]

dragen147 omg same😂

[@josed6739]

Alexia Aflallo Álvarez de Toledo because we have to solve it by its opposite so if it’s -2 we have to +2 or add 2. and if it’s +2 then we -2 or subtract 2

[@nasiphus]

i'm pretty sure your teacher fully understands what shes teaching, cause it's her job

[@beyoncegarrido3978]

I can’t believe I had to go this far to do my dang hw correctly

[@theNova99]

Mohamed Shahin *ThEn PaY aTtEnTiOn In ClAsS* but srsly. pay attention.

[@Kiakuh]

GamingPlazaAberin it’s not that easy when there are dickheads screaming their heads off in the back of class

[@TheKenpachi_]

Same, this is what happens when your absent for a day in middle school

[@antinoye973]

Beyoncé Garrido Ikr !!

[@antinoye973]

Achilles Louis literally me rn

[@alexdubois4912]

I wish my math teacher was as good as you

[@bryceb3796]

Alexander Dubois same

[@joshandserenaheiden4247]

same here lol

[@eecm1827]

same here

[@ChefGL1TCH]

Same my math teacher just gives us paper and says copy whats on the board then gives us a work sheet thinking we know how to do the work and then a week or 2 later gives us a test thing we know how to do the work when she is teaching lessons in 10 to 15 min rushing through stuff cause she likes to talk the entire class time and she cant do stuff visualy she just writes down what in the answer key and does a tiny bit of math in her head and calls herself a good math teacher

[@pumpersjd4834]

The best teachers i want to have is khanacademy and mathantics

[@ChessNetwork]

Nicely explained. :) Thumbs up!

[@neoarmstrongcyclonejetarms9326]

👍👍👍

[@imggt]

ChessNetwork am from future 10 years later you will have 420k subs and good at chess

[@imakevideos5186]

@@imggt lol

[@yoboy2619]

10 year old comment review 🙃

[@TieDyeGuy-rp6qs]

@@imggt I’m from 1 year in the future and chessnetwork has 466k

[@screamingmikewazowski5237]

Does anyone else think that ur getting much more work during online classes than u would during a regular class

[@discuamusic7401]

Bruh thats exactly my case right now

[@screamingmikewazowski5237]

KPop__is __생명saengmyeong ik i mean they say that because they “want the best from us” when we all know well that they didn’t do so much work back then (im assuming)

[@destinyaretrue2614]

Yes and its annoying 😭

[@linolopez3325]

Absolutely

[@screamingmikewazowski5237]

KPop__is __생명saengmyeong exactly they expect us to learn new stuff and yet we have no explaining and no help when we dont get it

[@screamingmikewazowski5237]

I hate everything... ESPECIALLY THESE ONLINE CLASSES AND ALGEBRA

[@discuamusic7401]

I totally agree

[@staceywright833]

Same

[@deniztaslicukur6226]

fr :(

[@superawesomecaillougod6664]

Your profile picture goes with that comment perfectly

[@shafiasif7247]

one of my online classes = 3 regular 75 minute periods so...

[@Maximillion11]

1. settings 2. speed 3. 1.25 4. Thank me

[@girllcosmic]

Thank you 😭

[@danieldnbt]

1.5 even

[@truthlennards8614]

C:D

[@p1zzapug]

i expected something funny. how dare u clickbait me

[@AstralGarden101]

O not doing this because this class is an hour 20 minutes and I want this to go as quickly as possible

[@josenemburg6112]

Khan had done so much for me and I thank you just want to point that out.

[@numbersletters2920]

1➗87=

[@dta-doubletimeanimations7689]

numbers letters get a damned calculator

[@baseballisgoat574]

Khan Academy is awesome! Being in 7th grade and online school makes learning a burden! Thank you so much!!!!

[@jegirveifbisnhekevdu]

Bro my math teacher says there is 3 different possible solutions for this

[@sleeken]

My math teacher just doesn’t explain stuff well he just tells us what to do for 5 minutes and then we have to do it on pencil and paper

[@Jacob-mx6ie]

CAN I GET A PRIVATE MATH CLASS?? AND CAN I PLEZ BE ADOPTED??

[@numbersletters2920]

1➗87=

[@tylersanchez9674]

mystery mystery hello

[@Luluuuuuuuu_12]

Mystery again

[@ro_lucas7812]

@@numbersletters2920 38?

[@malakl8137]

@@numbersletters2920 0.01234567901

[@freshappleseed6966]

Wow, this video is incredible! My teacher goes crazy fact and usually I can barely keep up. This is going to be a major help throughout the school year.

[@raz1n.r]

This WAS a really good video but iam still very confused 🤷‍♂️

[@subjectory]

same

[@Yui-vc6xh]

Yeah

[@screamingmikewazowski5237]

I didnt even pay attention im just looking at the comments plus i still dont get it

[@imtiazahmad2890]

@@screamingmikewazowski5237 thats probably why

[@mohamadalbakjaji1631]

.

[@AndalaASMR]

As someone who does struggle with adhd and reviewing math before going for a chemist degree, I super duper appreciate you showing us what the equations actually represent. It helps more than you know!

[@ratgirl5167]

Y’all are getting me through my algebra final tomorrow you’re the real MVP

[@Ethan-qe8pe]

How did you do

[@johnrosario4280]

My teacher could barely teach me this concept for 2 weeks, but this man right here helped me learn it in about 30 minutes! Thanks So Much! :D

[@aanyamehra1621]

Yo- my math teacher took 2 months (it’s still not done) it’s not that _she_ didn’t teach well it’s cuz of that one guy in class who asks nonsensical doubt for attention

[@janellafrancis5508]

Khan is my life saviour, I love these so much especially leading up to final exams.

[@cee9945]

Not even sure how my teacher is qualified 💀

[@supercoolgirl07]

fr😣

[@licespice0]

My teacher is overqualified and overwhelms us with an overly complex description of a very simple concept that takes all class

[@flower_sunshine2021]

they make it so easier for you to understand, really appreciate it🙏

[@opaldoesnotrhyme]

I'm in Algebra honors, but I never truly understood solving equations with variables (which is a huge part if algebra), until now. None of my teachers have explained it this well or thoroughly, and now I completely understand it. So thank you.

[@GYAOMFEN]

Are you still here

[@opaldoesnotrhyme]

@@GYAOMFEN I actually now teach algebra and am currently taking Differential Equations 2 in college!

[@lordofducks3430]

@@opaldoesnotrhyme Wow that's amazing!

[@ruhani1942]

When my math teacher talks gibberish for a whole class period, I know i can always count on Kahn Academy to make it clear

[@kariokiinoc]

Thank You, Thank you, Oh how I wish I had a teacher like this when I was in high school. In my day, you were not required to take any thing higher than basic math, I have never learned alegebra. I am now returning to school to earn a Bachelors Degree and this site is my new best friend !!!!!! Thank you again, I so appreciate all that you are doing.

[@yoboy2619]

You in college now huh?(comment review)

[@duplicpapers8753]

How are u now bro

[@mrhoolagan]

what program does he use to write all the stuff

[@grenenamek7669]

Ms paint

[@kat-sz6tq]

MrHoolagan I always ask that question! Do you think that program is great for digital art?

[@kyraphobic]

Katherine Gonzalez adobe draw is really good for digital art

[@MR_MIRTH]

ms paint is terrible for drawing, use autodesk krita or adobe and or anything else

[@villageronps5317]

Probably just MS Paint.

[@aliabdiiid2]

Hi My name is Ali and I, 'm a new person to the website. I want to learn Couse I really like Ken Academy because you are only the one take and teaching math very well and I understand you today and you are a genius and I love that and hope also anthers love you two so night e until I Succeeds

[@dionda77]

Thank you for these videos and the way u explain things makes it so much easier

[@milady1377]

all these people talking about how their teacher doesn’t even make sense, for me my teacher doesn’t even do the video herself 😆

[@bigupkyreace6213]

He makes it so simple. Thank you I have a big test coming up in September and this really helped

[@Ethan-qe8pe]

How did you do?

[@youngjames4067]

i switched schools and it was an entire year since i had learned how to do this, my teacher literally acts like its the most impossible thing on earth to simply run over this when you did it in 8 minutes. my knowledge is coming back a little so i really have to thank you

[@swiffer7243]

Thank you so much for the help I am a struggling algebra 1 student taking 9th grade early this help means a lot to me.

[@jewelbusch2161]

Khan Academy is AWESOME!!! It genuinely saved me, my online school didn't actually teach me how to do stuff so I turned here. LIFE SAVING!!!

[@shulaarmintor7644]

Tell me why whatever my algebra teacher says goes in one ear and out the same ear. (it does a little u-turn) But I actually learn from Khan academy.

[@Ethan-qe8pe]

Top 10 mysteries that will Never be solved

[@randomidiotonline5072]

Most likely because the videos work at a different pace, and only do one or two problems. In lessons, teachers tend to do several upon several questions, slowly helping you lose focus throughout. Well, that's my own experience and opinion. Maybe it's just because Khan academy is prerecorded, easily accessed, and you can skip time ahead as long as go back.

[@engineerered4577]

Just started this and didn't understand it, but this video really helped me what we are looking for in these kinds of problems, and how to solve.

[@NeonTuxedoCheesecake]

Hah we have a test today and I’m staying sick so this is helping me extra study for the retake 💀

[@Nadrealis]

Dear Mr. Khan, I would like to know what program you are using for this. I love the approach you're taking when you write out equations. I've looked through most of your math videos and love the format. Thanks.

[@neurodiversemom3578]

It would be nice to see the check on this equation

[@password8866]

Why did you choose to subtract 2n instead of subtracting 5n? This is were i get comfuse because i always choose to subtract or add from the wrong side you need to explain this step. Ive been on you're app and this part gets me stuck

[@sebzweebyt3974]

yes i dont understand

[@Tanker791]

thanks for the video tips i'm in 4th grade and since i want to learn algebra right now so i dont do it later in the future ill already know some of the awnser and this video and you'r other videos helped alot thanks khan academy for helping me learn good ways to study algebra.

[@auliiazzz]

great job!

[@coleboone6985]

@khan academy you are the best math teacher EVER

[@calebdowdle3369]

My gosh this excactly what i needed because im going to 7th grade but im still in 6th grade in 4th quarter and this really helps ive seen other videos that really help me you should be a online teacher NO joke this would help a lot of kids even kids who are home schooled and have problems with math you would be a great online teacher. Who agrees with me???????? comment yes or no

[@THOKZCHOMZ]

Good teacher 🔥💯

[@abeerbakshi]

You are the best Khan Honestly there is no one out there on youtube that is as helpful as you You have helped people getting from an b to maybe an a and this shows improvement which tells us that you are such a great help Thank you Khan

[@editaeditioncommedy2338]

ho my brother dot whisper

[@abosedebadmus1954]

I was struggling to understand how to do equations with polynomials and you helped me a lot!😀

[@reynacarpio1693]

wow this literally saved my life he explained step by step thank you

[@zuhrazozo3047]

Me: I want to cryyyyyyy!😭😢

[@polygames4712]

Showing the logic of why you do something in math makes such a huge difference. I don't understand how anyone can learn math in school it was just like now we do this following order of operations without explaining why so as soon as I encountered a problem that wasn't covered in the practice or mixed different concepts I wouldn't be able to figure it out

[@medhasarker6967]

Can i just quit school and just make this my school

[@s_xi1]

9 mins to explain how to solve equations with variables on both sides, Mind you my teacher have been trying to get this in my mind for the past 1 week and I have and exam tomorrow. Such a life saver thank you!

[@bigboi3339]

I’m still confused only because i have a math question thats looks different from the example question that’s he’s using, but it’s supposed to be the same steps that he uses to solve his...

[@BringBack500s]

Excellent as always, clear, made as simple as it needs to be to get to the result, and several ways to represent the problem.

[@the_big_nate5144]

I find it funny how a 9 minute video teaches me more than my teacher doing 3 periods

[@williamfairchild8973]

This video helped me so much with my homework thank you !

[@lailamccampbell487]

im a 7th grader taking algebra and ITS NOT IT BRUH. Highkey wanna scream-how the hell did i get into this class anyway i-???

[@Cummingwhales]

how likely are we gonna math past ninth grade

[@MrBonQuiQui-zv1wr]

@@Cummingwhales you get math up until 10th grade then its optional

[@MrBonQuiQui-zv1wr]

you start algebra in either 6 - 8th grade then move on to algebra 1 (9th grade) then algebra 2 (10th grade) or you can start early like i did which is algebra 1 in 8th grade with algebra 2 in 9th while I took pre-algebra in 6th.

[@stopbeingweird5335]

Did you at least have pre algebra?

[@IQ-rl2wx]

This video is so important as you will use these basics forever in numerous other subjects

[@jonathansmith1899]

Was it just me,or did 5:09 blow everyone's mind

[@ilanmoore6957]

it also blew my mind

[@templar01]

Dolphins Killed My Bird what blew your mind

[@tushardadhich2080]

Dolphins Killed My Bird it blew my mind

[@tushardadhich2080]

Dolphins Killed My Bird ya what did

[@wearetoxin5204]

We greatly appreciate you doing this for the world

[@jacobcourson4428]

Awesome.

[@tashmeebs]

This vid seems to be way more complicated than it should be... What I learned was to get all the X variables on one side and all none variables on the other. In other words, subtract the 5X from the right to the left, creating a negative 3X, and subtrating 3 from the left anf moving it to the right. Then you have negative 3X equals negative 5. When you divide the neg. 3 from the X, you get the answer: 5/3. It's real simple. Just remember to get all variables on one side.

[@kainoahthefrog]

I'm here because of my Algebra class... One word... BYE

[@8abyx]

An 8 minute video taught me more than 4 classes with my math teacher, thank you :)

[@theamazingmanski3001]

AnYonE 2019

[@jemcand9016]

2020

[@manicpixie8672]

2020 I'm from the future

[@curlyclouds8425]

no

[@kojoanobah3617]

thanks, bro you've helped me a lot

[@Hmc71206]

I thought I'd be fine with staring at a screen for 8+ hours for school. I was wrong. So so wrong. I can't feel my eyes.

[@myson291]

God bless this man. I have an algebra test tomorrow and probably would’ve failed without this

[@tobyfan3091]

Can u be my math teacher

[@belalfarid1484]

That was soooo simple, u organized my life!! OOO boy, my life is easier now, thxxx

[@evand.7352]

I don’t get it

[@bevman5364]

Thanks alot Khan academy i was really stumped on this stuff

[@mlyka17]

I’m watching a 9 year old video 😂😂

[@londy7328]

M L Y K A • same 😔🤦🏽‍♀️

[@mentalli._unstable]

I’m 12 n we r learning this rn😑😑

[@ellieebner9820]

I'm so glad I don't feel stressed anymore haha!

[@RikkuMaraschino]

My equation is: 2m = 24 + 3m I'm confused because of the single number on that side do I add?

[@TheJoey3590]

Just solve for m. There are different ways to approach this equation. The most simple way would be to subtract -3m to the other side so it becomes -m = 24. From here, it becomes m = -24. Another way would be to subtract 2m to the other side with 24 + 3m. Therefore the equation becomes 0 = 24 +m. The last step for this way is to subtract the 24 to the other side, giving you the answer : m = -24. The whole process involves trying to get the variable on one side all by itself.

[@starzthelimit3563]

You are a godsend! I finally understand this!!!! Everyone just says subtract this from both sides and add this to both sides without an explanation on why and I'm left thinking huh?????!!!!

[@jocelyndesantos2687]

to much info isn't there a shorter way to do this?

[@leagueofcarry1053]

2x+3=5x-2 -2x -2x 3=3x-2 +2 +2 5=3x Divide by 3 on each side 5/3=x AKA: x=5/3 takes less than 30 seconds once u get the hang of it

[@miguelduenas4146]

Jocelyn Desantos hi

[@oliviamiller4400]

Yes

[@jaco2092]

Yeah dont and move on with your life.

[@vincenttheodorearifin7305]

Its and education video

[@thecollector3377]

11 years later this video still useful

[@ernestchan5684]

I’m gonna fail my test

[@ForestwatcherTighnari]

I'm watching this the day before my test because I realized I ducked up drawing instead of taking notes

[@megamindgaming13]

Thank you so much this cleared everything up for me

[@dorianjp]

I don't understand anything.

[@andrewg7779]

He explained it really clearly if you dont understand you might want to go to solving equations with one variable

[@cassandraservo]

Same 😭😭 My test in Math is tomorrow but i don’t know anything 😪

[@분꽃나무]

22강 Algebra 1 - Unit 2 - L1 - 2/5 Unit 2 Solving equations & inequalities L1 Linear equations with variables on both sides 2/5 Intro to equations with variables on both sides 24.01.20 ~ 24. 7. Once you've 원슈브. ~하면 0:35 7. isolated 아이설릿 0:35 7. x you have 엑슈읍 0:36 0:35 12. want you just say, 워뉴저쎄이. 네가 ~라고 말하는 걸 원하지 않는다 0:52 27. And that would be 2:16 1. 0:01 involved 0:02 Let's try to solve a more involved equation. 렛츠 트라이르 솔브 어 모얼 인벌 디퀘이줜 이번엔 조금 어려운 방정식을 풀어 봅시다. (ㅈㄷㅂㅇ) 좀 더 복잡한 방정식을 풀어보도록 하겠습니다. ㆍㆍㆍ involved 인벌ㅂ드. 형. 4. 복잡한, 난해한, 뒤얽힌; 혼란한 1. 관여하는, 관련된, 연루된 /(사건 등에) 깊이 관련된, 말려든 ((in)) 2. 0:03 0:06 let 0:07 say 0:08 So let's say that we have, let's say that we have, let me think of a good, say we have 2x+3, 2x+3 is equal to, is equal to 5x, is equal to 5x-2. 2x+3=5x-2라는 식이 있습니다. 3. 0:23 0:24 So this might look a little daunting at first. 쏘 디스 마잇 루꺼 리를 또온띵앳 뻘슷 처음엔 조금 어려울 수도 있어요. ㆍㆍㆍ daunting 던팅, 돈팅. 벅찬, 주눅이 들게 하는 daunt 던트, 돈트. 타. 겁먹게[기죽게] 하다, 위압하다; (한)풀을 꺾다, 기세[기운]를 꺾다, 기를 죽이다 ㆍ (1)The task before us is a daunting one. 우리 앞에 놓인 과제는 벅찬 것이다. (2) They face a daunting challenge. 그들은 위압적인 도전에 맞선다. (3)Starting a new job can be a daunting prospect. 새 직장을 시작하는 것은 두려운 생각이 들게 하는 일일 수 있다. (4)The immensity of the task is daunting. 헤아릴 수 없이 엄청난 양의 일이 사람을 겁나게 한다. (5) She has the daunting task of ~. 그녀는 ~하는 벅찬 일을 맡고 있다. (6) daunt a bully with a look 설치는 자를 노려보아 위압하다. (7) be daunted by the difficulty 그 곤란으로 기가 꺾이다 (8)He is not a man to be daunted despite the immensity of the task. 헤아릴 수 없이 엄청난 양의 일이 있어도 그는 꺾일 사람이 아니예요. (9) She talked nothing daunted in front of them. 그녀는 그들 앞에서 조금도 기가 죽지 않고 이야기했다. (10) Every time I face my boss, I get daunted and can't even open my mouth. 나는 상사 앞에만 서면 위축돼서 입도 뻥긋 못한다 (11) There's no need to feel daunted. 괜히 주눅 들 필요 없다. (12) he wasn't daunted at all. 그는 끄떡도 안 했다. 4. (0:24) 0:25 both 0:26 we're 0:27 We have x's on both sides of the equation(s). We're adding and subtracting numbers. 위해브 엑시손 보옷 싸이즈퀘이줜. 즈월 애링 앤 썹트랙팅 넘벌. 양변에 x가 있고 수가 더해지거나 빼져있습니다. 5. 0:29 we'll 0:30 couple 0:31 How do you solve it? And I'll, we'll do it in a couple of different ways. 하우두유 솔비날 윌두이 커프러 디뻐런 웨이즈 여러 가지 방법으로 풀어 볼까요? (ㅈㄷㅂㅇ) 그리고 우리는 이를 몇 가지 다른 방법으로 수행할 것입니다. 😢6. 0:32 remember 0:33 want to 0:34 The, the important thing to remember is, we just want to isolate an x. 디, 디 임폴띵 르메머이(즈)위 저슷 워너 아이설레이런 엑스 여기서는 x를 한쪽으로 이항시키는 것이 중요합니다. (ㅈㄷㅂㅇ) 중요한 점은 단지 x를 분리하고 싶다는 것입니다. ㆍㆍㆍ isolate 분리[구분]하다, 격리하다, 고립시키다, 절연하다(전기), 미생물을 분리하다 transpose 이항하다 😢7. 0:35 x you've 0:36 0:37 /x 0:38 Once you've isolated an x, you've x equals something. Or x equals something. 원슈ㅂ 아이설릿 엑슈읍.엑스 이퀄 섬띵 그러면 x에 관한 식이 나와서 방정식의 해를 구할 수 있어요. (ㅈㄷㅂㅇ) x를 분리하면 x는 무엇인가와 같습니다. 즉, x는 무엇인가와 같습니다. 8. 0:39 / 0:40 You're, you're done. You've solved the equation. 유 쏘올 이퀘이줜 9. 0:41 go 0:42 You can actually go back and check whether that works. 처음으로 돌아가 검산을 할 수도 있죠. 10. 0:43 we're 0:44 0:45 on 0:46 to 0:47 0:48 So we're gonna do is just do a bunch of operations on both sides of the equation, to eventually isolate the x. 월거너두 이저스투어 뻔첩 오퍼레이션스 온 보옷 싸이저디퀘이션 투어.벤츄얼리 아이설레잇디 엑스 여러 단계를 거쳐 방정식의 x를 분리시킬 거예요. (ㅈㄷㅂㅇ) 우리가 할 일은 방정식의 양변에 대해 여러 가지 작업을 수행하여 결국 x를 분리하는 것입니다. eventually 부. 결국, 종내 11. 0:49 do 0:50 visualize 0:51 But while we do those, I actually want to visualize what's occurring. ~ 두 도우자 액츄 워느 비쥬얼라이즈 왓처커링 이 과정 속에서 어떤 일이 일어나는지 살펴볼 것입니다. (ㅈㄷㅂㅇ) 하지만 그렇게 하는 동안 실제로 무슨 일이 일어나고 있는지 시각화하고 싶습니다. 😭12. 0:52 oh 0:53 rules 0:54 s of 0:55 / 0:56 this is 0:57 isn't 0:58 Because I don't want you just say, oh what are the rules or the steps of solving equations. And I forgot whether this is allowed or that isn't allowed. 새론 워뉴저쎄이, 오 와라더루울 소더스텝.쏘썰빙 이퀘이젼.재나이뽈갓 웨더 디시저라럴 댓이즌터라욷 이렇게 방정식을 푸는 단계를 눈으로 살펴보면 어떤 것은 되고 어떤 것은 안되는지 이해할 수 있을 거예요. (ㅈㄷㅂㅇ) 왜냐하면 나는 여러분이 방정식을 푸는 규칙이나 단계가 뭐에요?, 그리고 이것이 허용되는지 저것이 허용되지 않는지 잊어버렸어요 라고 말하는 것을 원하지 않기 때문입니다. 13. 0:59 happening 1:00 be 1:01 1:02 If you visualize what's happening it'll actually be common sense what's allowed. 일렉츄비 카먼 쎈스 왓철라우드 어떤 것은 되고 어떤 것은 안되는지 이해할 수 있을 거예요. (My) 무슨 일이 일어나고 있는지 시각화하면 실제로 무엇이 허용되는지가 상식이 될 것입니다. 14. 1:02 1:03/we 1:04 right here 1:05 So let's visualize it. So we have 2x right here on the left-hand side. 좌변에 2x가 있습니다. 15. 1:06 1:07 So that's literally, that's x plus x. 16. 1:10 I'll 1:13 /1:14 And then you have plus 3, plus 3, I'll do is like this. ~ 그리고 3은 1+1+1로 쓸 수 있죠. 16. 1:18 thing 1:19 1:20 let 1:22 1:24 That's the same thing as 3, I could've drawn 3 circles here as well. Let me do the same color. 댓서 쎄임띵 애스뜨리, 아이 쿠릅 드론 뜨리 써클스 히얼 애즈웰. ~ 같은 수를 다른 방식으로 나타냈을 뿐이에요. (ㅈㄷㅂㅇ) 그것은 3과 같습니다. 여기에도 3개의 원을 그릴 수 있었습니다. 17. 1:25 /1:28 1:29 / 1:30 /so 1:32 And then that is equal to 5x. Do that in blue. That is equal to 5x's. So 1, 2, 3, 4, 5. 18. 1:37 /you 1:38 have to 1:39 when 1:40 Now I want to make it clear. You would never actually have to do it this way when you're solving the problem. 나워너 메이킷 클리어. 유욷네버 액츄얼리 해브투두읏 디스웨이 웨뉴얼 썰빙더 프라블럼 그리고 저는 분명히 하고 싶습니다. 문제를 해결할 때 실제로 이런 식으로 할 필요는 없습니다. 🥴19. 1:41 1:42 / 1:43 this 1:44 visualize 1:45 You would just have to do the algebraic steps. But I'm doing this for you so you could actually visualize what this equation is saying. 유우저스햅트두 어, 디 알저브레익 스텝스. 버람두잉디스뽀유소 유큳 액츄얼리 비쥬얼라이즈 왓디스 이퀘이저니 쎄잉 그냥 단계에 따라 계산해주면 됩니다. 지금 이렇게 푸는 이유는 과정을 보여주기 위해서에요. (ㅈㄷㅂㅇ) 대수적 단계만 수행하면 됩니다. 하지만 제가 여러분을 위해 이 작업을 하는 이유는 여러분이 이 방정식이 말하는 것을 실제로 시각화할 수 있기 때문입니다. 20. 1:47 1:48 2 1:49 / 1:51 1:52 The left-hand side is these 2 orange x's plus 3. The right-hand side is 5x minus 2. 더 렙탠 사이디즈 디즈 투 오렌젝시즈 플러스 뜨리. 더 롸잇핸 사이즈 빠이브엑스 마이너스 투 좌변은 2x+3이고 우변은 5x-2 였죠? 21. 1:53 1:54 let 1:56 1:57 So minus 2, we could write as minus-- let me do this in a different color, I'll do it in pink. 렛미 두디시너 디뻐런 컬러, 알두이린 핑크 -2는 분홍색으로 써 보겠습니다. 22. 1:59 So minus 2, I'll do as minus 1 and minus 1. -2는 -1, -1로 쓸 수 있어요. 23. 2:04 x's 2:06 on 2:07 same 2:08 Now we want to isolate the x's on, on the same side of the equation. ~ 엑시즈 언, 언 더 쎄임 싸이더ㅂ디퀘이줜 이제 양변에 있는 x를 한쪽 변으로 이항해 봅시다. 24. 2:09 So how could we do that? (ㅈㄷㅂㅇ) 그렇다면 어떻게 그렇게 할 수 있을까요? 😮25. 2:11 (My) Whether Well, there's two ways of doing it. 웨델스 투웨이저 두잉잇 (ㅈㄷㅂㅇ) 두 가지 방법이 있습니다. 26. 2:12 2:13 2x's 2:14 2:15 We could subtract these 2x's from both sides of the equation. 먼저 방정식의 양변에서 2x를 빼는 것입니다. .

[@분꽃나무]

. 27. 2:16 pretty 2:17 then 2:18 2:19 you'd 2:20 2:21 And that would be pretty reasonable. Because then you'd have 5x's minus 2x's. You'd have a positive number of x's on the right-hand side. 앤다우드비 프리리 리즈너블. 비커즈덴 유르해브 빠이브엑시즈 마이너스 투엑시스.유르해퍼 파지립 넘벌벡시손 ~ 5x에서 2x를 빼면 우변에 남는 x의 개수는 양수가 되겠죠. 27. 2:22 2:23 5x 2:24 Or you could actually subtract 5x from both sides 또는 양변에서 5x를 빼는 방법도 있어요. 28. 2:25 algebra 2:26 2:27 you will 2:28 That's what's neat about algebra. As long as you do legitimate operations, you will eventually get the right answer. 대첫츠 니러바 알저브라 송쥬두 리지미릿 아퍼레이션z, 유 윌 어벤츄얼리 겟더 롸잇 앤썰 등식의 매력은 옳은 과정을 거쳐 문제를 풀었을 때 항상 정답이 나온다는 것입니다. (ㅈㄷㅂㅇ) 이것이 대수학의 멋진 점입니다. 적합한 작업을 수행하는 한 결국 올바른 답을 얻을 수 있습니다. ㆍㆍㆍ neat 형. 간단하지만 훌륭한, 깔끔한, 뛰어난, 훌륭한 / 정돈된, 단정한, 말쑥한 29. 2:31 subtracting 2:32 both 2:34 So let's just start off subtracting 2x from both sides of the equation. 렛쩌슷따아럽 썹트랙팅 투엑스 쁘럼 보옷 싸이저디이퀘이줜 그러면 방정식의 양변에서 2x를 빼 봅시다. ㆍㆍㆍ start off 3. (…하는 것으로) 시작하다[처음에는 …이다] --> ~ + 전치사(with, by)/ ~ + 형 /~ + Ving ㆍ start off with some gentle exercises 약간 가벼운 운동으로 시작하다 started off by introducing ourselves 자기소개를 하는 것으로 시작했다 start off green but turn red later 처음에는 녹색이지만 나중엔 붉은색이 된다 started off working quite hard 처음에는 상당히 열심히 일을 했다 30. 2:35 that 2:36 remove 2:37 What I mean, that I mean we're gonna remove 2x's from the left-hand side. 이는 좌변의 x가 2개 사라진다는 의미에요. 🙄31. 2:39 2:40 left-hand 2:41 2:42 the 2:43 If we remove 2 han, 2x's from the left-hand side, we have to remove 2x's from the right-hand side. 이프위르뭅 ~ 위햅투르무웁 투엑시스쁘럼 더롸잇해앤 싸이드 좌변에서 x를 2개 지웠으므로 우변에도 x를 2개 지웁니다. 32. 2:45 so 2:46 Just right that. So what does that give us? ~ 쏘 워러즈땟 기버(숼)? 방정식은 어떻게 될까요? 33. 2:47 left 2:50 also 2:51 (us?) We're subtracting 2x's. 2x's from the left. And we're also going to subtract 2x's from the right. 버숼 썹트랙팅 투 엑시즈. 좌변에서 2x를 빼고 우변에서도 똑같이 2x를 빼줍니다. >> and we're 34. 2:54 what 2:54 our 2:55 simplify 2:56 Now, what is, what does our left-hand side simplify to? 좌변을 정리해 봅시다. (ㅈㄷㅂㅇ) 이제 좌변은 무엇으로 단순화되나요? >> our을 are로 생각했다 35. 2:57 2:58 / 2:59 3:00 We have(=We've) 2x plus 3 minus 2x. The 2x's cancel out. 2x + 3 - 2x 이므로 2x는 서로 소거되겠네요. ㆍㆍㆍ cancel out 상쇄되다/~을 상쇄하다 36. 3:01 So you're just left with-- you're just left with the 3. 그러면 3만 남게 됩니다. 37. 3:04 3:05 And you see that over here. We took 2 of these x's away. 위 툭 투오브 디젝시서웨이 이쪽 식에서 보면 x를 두 개 지웠기 때문에 ㆍㆍㆍ take away 제거하다, 치우다, 줄이다, 죽이다 80 take away 5 is 75. 80에서 5를 빼면 75이다. 38. 3:07 We're just left with the plus 1, plus 1, plus 1. +1+1+1 밖에 남지 않았습니다. 39. 3:10 3:11 5x 3:14 / 3:15 /5x's 3:16 And then on the right-hand side, 5x-2x. We have it over here. We have 5x's minus 2x's. You only have 1,2,3, x's left over. 우변을 계산해 봅시다. 5x-2x네요. 이쪽 식에서 보면 5개의 x에서 2개의 x를 뺐으므로 x는 3개만 남습니다. (ㅈㄷㅂㅇ) 그리고 오른쪽에는 5x-2x가 있습니다. 여기에 있어요. 5x-2x 가 있습니다. 이제 1, 2, 3x만 남았습니다. 40. 3:21 / 3:23 /3:26 3 is equal to 3x. And then you have your minus 2 there. You have your minus 2. 3은 3x와 같습니다. 그리고 거기에는 -2가 있습니다. 🥴41. 3:29 problem 3:30 write 3:31 So normally if you were to do the problem, you would just have to write what we have here on the left-hand side. 유우 젓스햅투 롸잇트 웟위해피얼온더 렙땐싸이드 보통 문제를 풀 때는 왼쪽 식처럼 계산해 주면 됩니다. (ㅈㄷㅂㅇ) 따라서 일반적으로 문제를 풀려면 여기 왼쪽에 있는 내용을 적어야 합니다. 🤯42. 3:32 can 3:33 we 3:34 So what can we do next? Remember, we want to isolate the x's. (My ear) So what can we do next? Well, we want to isolate the x's. 이제 x를 한쪽 변으로 몰아줘야 합니다. (ㅈㄷㅂㅇ) 그러면 우리는 무엇을 할 수 있나요? >> 왜 well이 아니라 remember인지 모르겠다 43. 3:36 3:37 right here 3:38 We have all of our x's on the right-hand side right here. x는 모두 우변에 있죠. 😭44. 3:38 3:39 off 3:40 hand 3:41 x's 3:42 /3:43 If we could get rid of this negative 2, off of the right-hand side, then the, the x's will be alone. They'll be isolated. 쁘기겟 리러디스 네거립 투, 오뻡떠 롸잇핸 싸이데니, 디 엑시즈 윌비 얼로운. 데을비 아이설레이릿. 우변의 -2를 없앨 수 있다면 우변에는 x만 남게 될 거예요. ㆍㆍㆍ off of 구어체. =on, from, off --> 공식적이거나 비즈니스 상황엔 적절하지 않다. 일상대화에서 사용. 45. 3:44 2 3:46 So how can we get rid of this negative 2, if we visualize it over here. This negative 1, this negative 1. 쏘 하우 캔위겟 리덥디스 네거립 투으, 쀠 비주얼라이짓 그러면 -2는 어떻게 없앨 수 있을까요? (ㅈㄷㅂㅇ) 그렇다면 여기서 시각화하면 어떻게 이 - 2를 제거할 수 있을까요? 이 -1, 이 -1. 46. 3:50 3:52 / 3:53 Well, we could add 2 to both sides of this equation. Think about what happens there. 웰 위큳 앧 투르 보옷 싸이저디시 퀘이줜 양변에 2를 더하면 되겠죠. 2를 더하면 어떻게 될까요? 🧐47. 3:55 2 3:56/ 3:57 / 3:59 So if we add 2, so I'm going to do (it) like this. Plus 1, plus 1. So you could literally see. We're adding 2. 쏘뿌이 앧 투, 쌈므느 두 라익띠스. ~. 슈 킬러럴리 씨월 애링 투 (ㅈㄷㅂㅇ) 따라서 2를 더하면 이렇게 됩니다. +1 +1. 문자 그대로 볼 수 있습니다. 48. 4:00 4:01 / 4:03 And then we're going to add 2 to the left-hand side.1 plus, 1 plus. 에눨그느 앧 투우드더 렙탠 싸이드. (ㅈㄷㅂㅇ) 그런 다음 왼쪽에 2를 더할 것입니다. 49. 4:05 /4:06 /so 4:08 What happens? Let me do it over here as well. So we're gonna ~. (ㅈㄷㅂㅇ) 여기에서도 할게요. 50. 4:11/ 4:13 / 4:17 4:20 /4:22/ 4:23 So what happens to the left-hand side? 3 plus 2 is going to be equal to 5. And that is going to be equal to 3x - 2 + 2. These guys cancel out. You're just left with 3x. 51. 4:26 /4:28 /4:31 And we see it over here. We have the left-hand side is 1 plus 1 plus 1 plus 1 plus 1. We have 5 1's, or 5. 위입떠 렙탠 싸이드 원 플러스 ~. 오른쪽 식에서 보면 좌변에 1이 다섯 번 더해졌죠. 1이 다섯 개 있으므로 5와 같습니다. (ㅈㄷㅂㅇ)그리고 우리는 여기에서 그것을 봅니다. 왼쪽에는 1+1+1+1+1이 있습니다. 5개의 1, 즉 5가 있습니다. 52. 4:33 we 4:34 / 4:37 4:38 4:40 / 4:41 4:42 And the right-hand side, we have the 3x's right over there. And then we have the negative 1, negative 1, plus 1, plus 1, negative 1, these cancel out. They get us to 0. They cancel out. 우변에는 x가 3개 있고 -1 -1과 +1 +1은 소거됩니다. 즉, 0이 되는 것이죠. (ㅈㄷㅂㅇ) 그리고 오른쪽에는 바로 저기에 3개의 x가 있습니다. 그리고나서 우리는 -1, -1을 갖게 됩니다. +1, +1. -1, 이것들은 상쇄됩니다. 🙄53. 4:44 / 4:47 So we're just left with 5 is equal to 3x. So we have 1, 2, 3, 4, 5 is equal to 3x. 쏘월저슷 어뿟 빠이브 이즈 이퀄투 ~ 이제 5는 3x와 같습니다. 54. 4:50 clear 4:51 so 4:54 / 4:56 4:58 Let me clear everything that we've removed, so (it) looks a little bit cleaner. Let me clear that out, that let me clear... 오른쪽 식에서 계산했던 과정을 지워 볼게요. (ㅈㄷㅂㅇ) 제거한 모든 항목을 지워서 좀 더 깔끔하게 보이도록 하겠습니다. ㆍㆍㆍ clear (A에서) (B를) 치우다 Clear all those papers off the desk. 책상에서 그 서류들 모두 치워요. I had cleared my desk before I left. 나는 나오기 전에 책상을 말끔히 치웠다. 55. 5:00 5:01 /5:02 / 5:04 / edit 5:06 These are all of the things that we've removed. Let me clear that out. And then let me clear that out, like that. Edit. Clear. 디자 올러더띵샛 위 르무브드. 여기도 지워주고 이 부분도 지우겠습니다. (ㅈㄷㅂㅇ) 이것들은 우리가 제거한 모든 것입니다. 그 점을 분명히 하겠습니다. 그런 다음 그것을 정리하겠습니다. 편집 완료. ㆍㆍㆍ clear out (~을 없애고) 청소하다 clear out a drawer / room 서랍, 방을 청소하다 We cleared out all our old clothes. 우리는 헌 옷을 모두 없앴다. I found the letters when I was clearing out. 짐 정리를 하다가 그 편지들을 발견했다. .

[@분꽃나무]

56. 5:09 /5:12 5:13 /() 5:14 5:17 /5:19 So now we are just left with 1, 2, 3, 4, 5. Actually let me move this over. (So edit. Cut. Edit paste) So I could just move this over, right over here. ~ 액츄렛미 무브 디스오벌. ~ 쏘아이크 저스무브딧스 오벌, 롸잇 오벌 히얼 이제 좌변에는 1이 다섯 개 남아 있습니다. 1+1을 좀 가까이 옮겨 볼게요. (ㅈㄷㅂㅇ) 그래서 이것을 바로 여기로 옮길 수 있었습니다. ㆍㆍㆍ paste 3. (텍스트를 오리거나 복사하여 다른 곳에 갖다) 붙이다 1. 풀로 붙이다, 종이에 풀을 붙여 만들다 / 명. 붙이는 풀, 밀가루 반죽, 반죽한 것; 이긴 흙; 연고(軟膏); 과일의 설탕졸임; 고약; 치약(toothpaste); cut and paste 오려 붙이다 57. 5:22 5:24 / 5:26/ 5:28 5:29 they have 5:30 We now have, we now have 1, 2, 3, 4, 5. These are the 2 that we added here, is equal to 3x. These guys canceled out. That's why we have nothing there. 디자더 투댓 위애릿 히얼, ~ 좌변에는 1이 다섯 개 있죠. 이 부분은 양변에 더해준 2입니다. 우변에서 더해준 2는 소거되어 아무것도 남지 않았습니다. (ㅈㄷㅂㅇ) 이제 1, 2, 3, 4, 5가 있습니다. 58. 5:31 we 5:32 5:35 Now to solve this, we just divide both sides of this equation by 3. 나우 투 쏘올디스, 위 저슷 드바읻 보옷 싸이저디스이퀘이줜 바이 뜨리. 이제 양변을 3으로 나눠 봅시다. 😶59. 5:36 5:37 5:38 /5:39 5:40 5:41 This (is) gonna be a little hard to visualize over here. But if we divide over here both sides by 3, what do we get? 디스 고느비 리를 하알투 비주얼라이즈 오버 히얼. 버르뿌이 드바읻 오벌히얼 ~ 워루위겟? 조금 어려울 수도 있어요. 양변을 3으로 나누면 어떻게 될까요? (ㅈㄷㅂㅇ) 여기서는 시각화하기가 조금 어려울 것입니다. 하지만 여기서 양변을 3으로 나누면 무엇을 얻게 될까요? >> but if we, what do 60. 5:43 5:44 / 😅5:45 5:46 by 3 5:47 x was 5:48 We divide the left by 3. We divide the right by 3. The whole reason why we divided by 3 is because the x was being multiplied by 3. 위 드바이더 렙ㅍ트 바이 뜨리. 위 드바이더 롸잇 바이 뜨리. 더'홀 리즌 와이위드바읻 바이뜨리 이즈 비코지 엑숴즈비잉 멀티플라이 바이 뜨리. >> we, the x, 61. 5:51 /5:53 5:54 5:57 3 is the coefficient on the x. Fancy word, it literally just means the number multiplying the variable, the number we're solving, the variable we're solving for. 뜨리 이즈디 코어삐션 온디엑스. 뺀시 월 일리러럴리 저슷 민서 넘벌 멀티플라잉 더 베리어블. 3은 x의 계수입니다. 멋진 단어로, 문자 그대로 변수에 숫자를 곱하는 것을 의미합니다. 62. 6:00/ 6:02 / 6:05 So these 3's cancel out. The right-hand side of the equation is just x. The left-hand side is (the) 5/3. ~ 더 롸잇 핸 싸이럽디이퀘이줜 ~ 더 렙탠.싸읻 이즈 빠입 떨즈 (ㅈㄷㅂㅇ) 우리가 풀고 있는 숫자, 우리가 풀고 있는 변수. 63. 6:08 you could 6:09 /6:10 6:11 /I now 6:13 the value 6:15 So 5/3, you could say x is equal to 5/3. This is different than everything we've seen so far. I now have the x on the right-hand side, the value on the left-hand side. ~ 유큳쎄 엑시지퀄르 빠입 떨즈. 디싯 디뻐런댄에브리띵 위이씬쏠빠알. 아이나우 해ㅂ디 엑손더 롸잇해앤 싸이드, ~ 따라서 5/3=x가 됩니다. 지금까지 봐왔던 식과 다르게 x가 우변에 있고 수가 좌변에 있죠. >> than 64. 6:16 6:17 exact 6:18 same 5/3 6:20 6:21 thing as 6:22 That's completely fine. This is the exact same thing as, the same 5/3 is equal to x the same thing as same x is equal to 5/3. ~. 디스 이즈더 이그젝 세임띵 애즈, 더 쎄임 빠입떨지 지퀄르 엑서 쎄임띵 애쎄임 엑스이즈이퀄투 빠이브떨즈 순서는 상관없습니다. x=5/3와 같은 의미에요. (ㅈㄷㅂㅇ) 이것은 5/3이 x와 같다고 말하는 것과 x가 5/3과 같다고 말하는 것과 똑같습니다. 🧐65. 6:24 6:25/ 6:26 /we 6:27 6:28 Completely equivalent. Completely equivalent. We sometimes get more used to this one but this is completely the same thing. 컴플릿리 이퀴이블른트. 컴플릿리 이퀴이블. 순서는 상관없습니다. x=5/3와 같은 의미에요. 두 식의 모양은 다르지만 같은 것을 의미해요. (ㅈㄷㅂㅇ) 완전히 동일합니다. 우리는 때때로 이것에 더 익숙해지지만 이것은 완전히 같은 것입니다. ㆍㆍㆍ equivalent 형. (가치·의미·중요도 등이) 동등한, 맞먹는 명. ~ of/to (…에) 상당[대응]하는 것, 등가물 66. 6:31 write 6:32 mixed 6:33 number if 6:34 6:35 3 6:36 6:37 with 6:38 Now if we wanted to write this as a mixed number, if we want to write this as a mixed number, 3 goes into 5 one time with remainder 2. 나 삐워니르 롸잇 디스 애즈 에이 믹스드 넘벌, 이프위워너 롸잇 디새저 믹스드 넘벌, 뜨리 고진드 빠이브 원타임 욷르메인덜 투 대분수로 한번 나타내 봅시다. 3은 5에 한 번 들어가고 2가 남죠. (ㅈㄷㅂㅇ) 이제, 이것을 대분수로 쓰고 싶다면, 3이 5에 한번 들어가고 나머지는 2가 됩니다. ㆍㆍㆍ mixed number 대분수 = mixed fraction 가분수 improper fraction, top-heavy fraction 진분수 proper fraction go into …에 들어가다(=enter). remainder 리메인덜(미), 르메인다(영). (뺄셈·나눗셈의) 나머지 67. 6:39 6:40 / 6:42 So it's going to be 1 2/3. ×2 소스 고느비 원앤 떨즈. 소스 고잉느비 ~ 따라서 1 2/3이 됩니다. 68. 6:44 also 6:45 6:47 /6:49 for you 6:50 back 6:51 6:52 (2/3.) So we could also write that x is equal to one and two thirds. I'll leave it up for you to actually substitute back into this original equation. 투떠얼소 위큳올쏘 롸잇땟 엑스 이즈 이퀄투 ~ 떨자을 리비럽뽀유 드액츄얼 썹티튯 빼애킨투 디스리지널 퀘이젼. 이를 x = 1과 2/3라고 쓸 수도 있어요. 해를 원래 식에 대입해서 직접 검산해 보세요. (ㅈㄷㅂㅇ) ~. 그리고 저는 여러분이 실제로 이 원래 방정식으로 다시 대체할 수 있도록 남겨두겠습니다. ㆍㆍㆍ substitute 역할을 대신하다, 대리하다; [化]치환하다 69. 6:53 And see that it works out. 앤씨대릿 워얼싸. 그리고 그것이 효과가 있는지 확인하십시오. 70. 6:54 visualize 6:55 how did 6:56 6:57 Now, to visualize it over here, you know, how did he get 1 2/3, let's think about it. 하우디디겟 원앤 떨 이제 오른쪽 식에서 1과 2/3을 구해 볼까요? (ㅈㄷㅂㅇ) 이제 여기 시각화를 위해 그가 어떻게 1 2/3을 얻었는지 생각해 봅시다. 71. 6:58 6:59/ 7:01 Instead of doing 1, I'm going to do circles. I'm going to do circles. 쎄럽 두잉 원 암므느두 써클스. 아이엠 고잉투두 써클스. 72. 7:03 7:04 Actually even better, I'm going to do squares. 액츄이븐 베람므느두 스퀘얼스 (ㅈㄷㅂㅇ) 사실 더 좋은 건 정사각형을 할 거예요. 71, 72. 정사각형을 이용해서 설명해 보겠습니다. 73. 7:06 So I'm going to have 5 squares on the left-hand side. 쏘 암므느 해브 빠이브 스퀘얼존더 렙탠 싸이드 그래서 저는 왼쪽에 5개의 정사각형을 갖게 될 겁니다. 74. 7:08 /7:11 / 7:19 7:20 / 7:22 I'll do it in this same yellow color right here. So I have 1, 2, 3, 4, 5. And that, that is going to be equal to 3x's. x+x+x. 아두이린디스 쎄임 옐로우 컬러. 쏘아브 ~. 앤댓, 땟이즈 고잉투비 이퀄투 뜨리엑시스. ~ 75. 7:25 7:29 / Now we're dividing both sides of the equation by 3. We're dividing both sides of the equation by 3. 나우 월드바이링 보옷 싸이저디퀘이줜 바이 뜨리. 🙄76. 7:32 here 7:33 sides 7:34 Actually that's where we did it up here, we divided both sides by 3. 액슈댓츠 워리디덥피얼, 위 드바이릳 보옷 싸이즈 바이 뜨리. 오른쪽 식에서도 양변을 3으로 나눠주었죠? (ㅈㄷㅂㅇ) 사실 여기서는, 양변을 3으로 나누었습니다. 77. 7:34 /7:35 /7:37 x's 7:39 / 7:41 How do you do that? Right-hand side's pretty straightforward. You want to divide these 3 x's into 3 groups. That's 1, 2, 3 groups. 1, 2, 3. 우변은 쉽게 나눌 수 있습니다. x가 세 개를 세 묶음으로 나누면 이렇게 되겠죠? 5는 어떻게 똑같이 세 묶음으로 나눌 수 있을까요? 아까 답을 구했듯이 한 묶음은 1과 2/3이 될 거예요. (ㅈㄷㅂㅇ) 그럼 어떻게 할까요? 우변 쪽은 꽤 간단합니다. 이 3개의 x를 3개의 그룹으로 나누고 싶습니다. 1, 2, 3그룹입니다. ㆍㆍㆍ straightforward 간단한, 쉬운, 복잡하지 않은 (=easy) / 솔직한 .

[@분꽃나무]

78. 7:43 7:44 / 7:45 7:46 / 7:48 / 7:49 7:50 so 7:51 /7:53/ 7:56 Now, how do you divide 5 into 3? And they have to be thought through even groups. And here tell, the answer tells us. Each group is going to be 1 2/3. So, 1 2/3. So (it's) going to be 2/3 of this, the next one. And then we're going to have 1 2/3. 5는 어떻게 똑같이 세 묶음으로 나눌 수 있을까요? 아까 답을 구했듯이 한 묶음은 1과 2/3이 될 거예요. 1과 두 번째 정사각형의 2/3를 합치면 1과 2/3이 됩니다. (ㅈㄷㅂㅇ) 이제 5를 3으로 어떻게 나누나요? 그리고 그것들은 짝수 그룹을 통해서도 생각되어야 합니다. 그리고 그 답은 우리에게 말해줍니다. 각 그룹은 1 2/3이 될 것입니다. 따라서 1 2/3입니다. 그래서 이것은 다음의 2/3가 될 것입니다. 그리고나서 우리는 1 2/3을 갖게 될 것입니다. 79. 7:58 /7:59 8:00 / 8:01/ 8:04/ 8:08 So this is 1/3. We're going to need another. Another 1, so this is 1 1/3. We're going to need 1 more 1/3, so this is going to be right here. And then we're left with 2/3 and 1. 두 번째 정사각형은 1/3이 남고 세 번째 정사각형 전체와 네 번째 정사각형 1/3을 가져오면 1과 2/3이 됩니다. (ㅈㄷㅂㅇ) 그래서 이것은 1/3입니다. 우리는 또 다른 것이 필요합니다. 또 1이 있으니 1 1/3이 됩니다. 1/3이 더 필요하므로 이것이 바로 여기에 있을 것입니다. 그리고 2/3과 1이 남습니다. 80. 8:10 / 8:12 So we've broken it up into 3 groups. This right here. 이렇게 5를 세 묶음으로 나눴습니다. 81. 8:13 /8:14 / 8:19/And then 8:20 8:23 8:24 /8:27 Let me make it clear. Let me make it clear, this right here is 1 2/3. 1 2/3. And then this right here this is 1/3. That's another 1/3, so that's 2/3, and then that's 1 right there. So that's 1 2/3. 좀 더 깔끔하게 정리해 볼까요? 여기는 1과 2/3이고 그리고 여기는 1/3이고 여기 1/3이 또 있습니다. 그리고 1이 여기 있으므로 다 합쳐서 1과 2/3이 됩니다. (ㅈㄷㅂㅇ) 명확하게 말씀드리겠습니다. 분명히 말씀드리자면, 이것은 바로 1 2/3입니다. 1 2/3. 그리고 바로 여기 이것이 1/3입니다. 그게 또 1/3이니까 2/3이 되고, 그 다음엔 바로 1이 되는 거죠. 그럼 1 2/3이군요. 82. 8:29 And then finally this is 2/3 and this is 1, so this is 1 2/3. 마지막으로 여기는 2/3이고 여기는 1이므로 1과 2/3입니다. (ㅈㄷㅂㅇ) 그리고 마지막으로 이것은 2/3이고 이것은 1이므로 이것은 1 2/3입니다. 83. 8:34 So when you divide both sides by 3, you get 1 2/3. 이렇게 양변을 3으로 나누면 (ㅈㄷㄱㅇ) 따라서 양변을 3으로 나누면 1 2/3이 됩니다. 84. 8:39 8:40/ 8:44 / 8:46 Each, each section, each, each bucket, is 1 2/3 on the left-hand side. On the left-hand side, or 5/3. And on the right-hand side we just have an x. 좌변의 한 묶음에는 1과 2/3 즉, 5/3가 들어갑니다. 우변의 한 묶음에는 x가 한 개 들어가죠? (ㅈㄷㅂㅇ) 각 섹션, 각 버킷은 좌변에 1 2/3입니다. 좌변은 즉, 5/3. 그리고 우변에는 x만 있습니다. 85. 8:48 8:49 So it still works. A little bit harder to visualize with fractions. 끝났습니다. (ㅈㄷㅂㅇ) 그래서 여전히 작동합니다. 분수를 시각화하기가 조금 더 어렵습니다. .

[@분꽃나무]

ㆍ 1~26 : 1, 2, 3 5. solve it? And I'll, 솔비날 0:29 6. the important thing to remember is, we 디 임폴띵 르메머이(즈)위 0:32 7. Once you've 원슈브. ~하면 0:35 7. isolated 아이설릿 0:35 7. x you have 엑슈읍 0:36 0:35 12. want you just say, 워뉴저쎄이. 네가 ~라고 말하는 걸 원하지 않는다 0:52 12. rules or the steps of solving equations 루울 소더스텝.쏘썰빙 이퀘이젼 0:54 12. this is allowed or that isn't allowed. 디시저라럴 댓이즌터라욷 0:57 0:58 13. it'll actually be 일렉츄비 1:00 0:59 13. what's allowed. 왓철라우드 1:01 0:59 18. You would never actually have to do 유욷네버 액츄얼리 해브투두읏. 실제로 ~할 필요는 없다 19. You would just have to do 유우저스햅트두. 그냥 ~하면 된다 1:41 25. Well, there's 웨델스 2:11 27~55 : 1, 27. And that would be 앤다우드비 2:16 27. You'd have a 율햅, 윧해뻐 2:18 2:20 28. That's what's 대첫츠 2:25 28. As long as you do 송쥬두 2:26 29. So let's just start off 렛쩌슷따아럽 ~으로 시작해 봅시다 2:30 2:31 46. sides of this equation 사이저디시 퀘이줜 3:52 47. So I'm going to 쌈므느 3:56 47. So you could literally 슈 킬러러리 3:59 48. we're going to 워그느 >> 여기서는 앞의 and then과 연음되어 워가 제대로 발음x 48. 2 to the 투르더, 투드더 48. And then we're going to 애눨그느 4:01 56~77 : 1, 2, 64. This is the exact 디시지 이그젝 6:17 64. same 5/3 is equal to 빠입떨지 지퀄르 6:20 64. x the same thing as same 엑서 쎄임띵 애쎄임 6:21 66. Now if we wanted to 나 삐워니르 6:31 66. 3 goes into 5 one time with remainder 2. 3은 5에 한 번 들어가고 2가 남는다 6:36 68. 2/3. So 투떠얼소 6:44 70. how did he get 하우디디겟 6:56 74. I'll do it in this 아두이린 디스 7:08 77. How do you do that? 하류두댓? 7:34 78~85 : .

[@emmalynn18]

sorry, i still dont understand

[@itsurmomoclock6503]

ty I’m currently crying on the night before the test 🤘😀

[@DarkenedLights666]

You should try to explain slower

[@miamiric6051]

You can slow down the video and he repeats things about 50 times...

[@3SN201]

Just go to settings and change the playback speed

[@malaikas389]

Superb explanation.

[@jonathanzapata358]

yes.. thank you Khan Academy.

[@susantangel5448]

Thank you sooooooooo much. I'm going into advanced algebra and need this so bad.

[@saptadweepaganguly8297]

this is actually practical for a 11-year-old who has been just introduced to algebra...the video's awesome...😊😍😉😄;🤩🙂🎉

[@binnebambaronn5047]

ur so good at explaining!

[@ProfessorTheNinjaAJ]

This video was a big help. Thank you so much!

[@Seannoostrich]

This is a life saver thank you so much

[@coleboone6985]

Kahn acadomy explains everything perfect

[@Nexluls]

This guy is very good at teaching👍

[@smartapplesuperkids6774]

This is a great video on solving equations with variables on both sides.

[@mfkrmaggot2755]

11th grader here. I never understood school algebra, your videos help a lot!

[@ШубанТурманов]

Sal, the god of explaining math.

[@JustThatGuy95]

Thx a lot I have been unmotivated for a while bc of depression and other related issues Did rlly helped me have a huge comeback.👍🙌🙌🤙🤙

[@priaatplay6207]

khan academy is so helpful. makes it so much easier than how my teachers explain

[@FireStrikeKiki]

Accelerated math has been hard, so this is a lifesaver

[@rakelaa7234]

Hello dear teacher!!! I don’t quite understand which side to start working with, for example you choose to start with 2x and I see that some people start on the left and some on the right. Please explain, I know there’s something I’m missing help please!!!!

[@ndowg]

same

[@siddarthg6088]

ur so helpful thank you

[@ariannee5107]

Totally not me using a different formula but still got the correct answer

[@skittygacha5481]

Thankyou so much for helping me abd doing what my math teacher couldn't