Algebraic Equations With Variables on Both Sides

[@m.b.3488]

This guy deserve infinite respect for his work for the humanity.

[@JacksonDavis-m9f]

Fr like usually math teachers take like months and weeks to fully explain algebra when this guy made it to like 1 or 2 days

[@JacksonDavis-m9f]

@bookymydoor Fair point

[@livewithashley]

i just completed the Checking Comprehension and i’m so proud of myself. Don’t know if anyone is here in 2024 and has always been ridiculed for not being good at math, you ARE good at math, math IS interesting and you don’t have to be afraid! You can do it all! God is with you❤

[@ShohsanamShonazarova]

And you are kind

[@fatimeh0]

❤

[@Kitcat_myce]

science on top

[@dontstealmydiamondsv3156]

I had some trouble here because I somehow forgot how the distributive property works. If someone had such a misunderstanding in a traditional schooling program, it could go unnoticed and spiral, which is unfortunately all too common. It's such a shame that so many people can fall through the cracks and miss out on a whole world of knowledge, but it's all the more reason why I'm so grateful for the efforts of online educators like you and Khan Academy.

[@Shwetang.]

I won’t steal your diamonds sorry 😞

[@piyushyadav79244]

Mee also 😢 but I have been sole that 👍 🙃😊 🤡 and now I am going to give it to you 🙂 back 😅😊👍

[@OkSid300]

I never thought in my life that will be getting dopamine charge form solving EQUATIONS! But you made it happen. You are the Jesus of teaching.

[@apostolosfilippos]

I wanted to study differential equations but your videos are so fun, I decided to binge watch the whole playlist. Always thing to learn better by repeating.

[@ReadingtheBibleforever]

Professor Dave my teacher was so monotone and her class was boring so I couldn’t focus and stuff like that and I’m relearning it I’m really really glad you have a playlist and your not monotone or boring I need algebra to get all the way up to calculus for my job since calculus is really important for my job I would love to have

[@joshfoster-zj1ul]

i subscribed after this video. i started from the beginning. i have a college degree in environmental science but i know math is an engine you must use constantly or you lose it. when i saw that you took care to not just program rules into teaching but rather explain the why i knew you were a solid teacher. the explanation in the video of the method was worth the subscription. i will make sure to finish to the end of all of your videos for re teaching.

[@AzuroTemplar]

This is waaaaaaay less harder than i remembered, not sure if it has something to do with motivation or simply maturity. Regardless once again, cheers for the video!

[@codexcodexcodex]

Me too

[@nanimo943]

same thoughts here

[@procrastinates]

Professor Dave is just a great teacher. Math will seem a lot harder if you have a bad teacher.

[@ShohsanamShonazarova]

3x-2=5x+8 3x-2+2=5x+8+2 3x=5x+10 3x-5x=5x+10-5x -2x=10 X=10/-2 X=-5 2(x+6)=4(x+1) 2x+12=4x+4 2x-4x+12=4x-4x+4 -2x+12=4 -2x+12-12=4-12 -2x=-8 X=-8/-2 X=4 (7x-7)/3=14 7x-7=14×3 7x-7=42 7x-7+7=42+7 7x=49 X=49/7 X=7 (5x-4)/3=2(x+2) 5x-4/3=(2x+4)×3 5x-4=6x+12 5x-4+4=6x+12+4 5x=6x+16 5x-6x=6x-6x+16 -x=16 x=-16

[@justadudeonyt]

very helpful dud thanks .

[@lolkage3136]

I'm enjoying your teaching process.

[@kartikchauhan3692]

At 4:02 this is applicable to addition and subtraction as well just have to inverse the sign example : 2x-6=7 , -6 goes to other side as 6 , 2x=7+6 , 2x=13 , x=13/2.

[@SwollFullReady2Roll]

Amazing teaching on this subject. I'm learning more in 7 minutes than I did in most of high school.

[@redbaron1901]

Thanks!

[@loveurself764]

Love the videos! Makes it so much easier and less stressful to learn algebra!

[@viralnews1697]

Great Work Professor Dave

[@kantitsamystery6328]

You're absolutely right about practice. I'm years and years out of practice. But I've gone back to school for electrical and need to brush up on my algebra before I take on trigonometry so I can begin to understand the formulas for AC wave functions and such. This is a big help for me.

[@Adam-lf1hz]

All the comprehension questions where easy to perform expect the bottom right one which took some time and I had to Wright down and solve the equation on paper but I still got it, great video!

[@ignacioleikis1784]

Generally speaking, what REALLY helps simplify difficult equations is moving ALL of the contents from one side of the equation to the other, and making the entire equation = 0. You can proceed from that point.

[@rushikeshkadam8773]

i stil cant believe this things can be so easy salute to professor dave

[@osrock6262]

3:05 "Well that problem took three steps, which is certainly more than one" Subtle humor applied c:

[@Anon01X]

Hey Professor Dave, I know these videos are old and you're busy but why don't you multiply the (3-3x) with 4 as well? Since we had to do that for the right why didn't we do that for the left? I understand that we multiplied the right with 4 to cancel the division by 4 taking place on the left but then why do we not multiply. I think I get it actually, since we actually did divide 3-3x by 4 and then we multiplied that back by 4 to get our original answer. Never mind, just needed to type it out!

[@myonlineclasses3651]

It could've been better if sir Dave added some calculations at the end of the Q & A instead of just giving the answer itself. #3 of Q&A, I got the answer of X=9 if I were to use the reversed PEMDAS. However, using the MD first, then use AS afterwards would give me X=7 which was given as the correct answer in the video. This is rather weird.

[@RahilahJalloh-nn2mn]

Surely

[@anthonystark6215]

Thank you, Professor!

[@EducatorSharmin]

It is really helpful for Students. Can you make more video about Math?

[@ProfessorDaveExplains]

i'm currently making them by the dozens! go to my mathematics playlist and you'll see.

[@EducatorSharmin]

Thanks

[@RahilahJalloh-nn2mn]

​@ProfessorDaveExplains if I may, would you please make comprehension problems a little bit more than usual

[@RahilahJalloh-nn2mn]

​@@ProfessorDaveExplainsI currently have difficulties in topics like surds and logarithim

[@MANVILAALASA]

you , you right there ,you are a life saver

[@MiltonRosso]

These are now my favorite videos.

[@Fafa65125]

Thanks Professor Dave ❤

[@laurentiul100]

I've seen 25 vids without stopping, 10 vids a day and i am 2 weeks and a bit away from learning all maths!!

[@redicendia1355]

5x-4=6(x+2) 5x-4=6x+12 5x=6x+16 6x=5x-16 x=-16 im gonna check my answer edit: yay i got it right

[@spencerpanes8748]

Why did you switch 5x to 6x?

[@SimonDusk6453]

ery noice

[@jayeteee7149]

Hello professor dave! I’m having trouble in question number 1 in comprehension (3x-2 = 5x + 8) can you please explain how did you get the answer?

[@ProfessorDaveExplains]

subtract 2x from both sides and then subtract 8 from both sides and then divide both sides by 2!

[@jayeteee7149]

Thank you professor dave!

[@adrianclark2734]

@@ProfessorDaveExplains I'm literally confused, I know this is easy stuff but to me, I'm getting 3x-2=5x+8 (subtract 2x from both sides) -2=3x+8 (subtract 8 from both sides) -10=3x (divide both sides by 2) -5=1.5x?? somehow its not getting through to me, please help?

[@marithmae]

@@adrianclark2734 Maybe if you see it written out it out it'll help! 3x - 2 = 5x + 8 (subtract 3x from both sides) -2 = 2x + 8 (Subtract 8 from both sides) -10 = 2x (Divide both sides by two) -5 = x I believe when he replied to the above comment and said to subtract 2x, that was a typo. You need to subtract 3x from both sides in the first step in order to only have the variables on one side of the equation.

[@adrianclark2734]

@@marithmae ahhh haha, yeah that makes sense now, thank you 😊

[@ljr6490]

1:00 SADMEP!

[@cjnuwu]

Teacher : talk a contents about one week This guy : 6 minutes

[@letustravel2685]

toooop teacher i think your the best man keep going

[@Kalkazaar]

You're a hero.

[@LungmichonAngel]

Beatiful work professor dave

[@samuel-j9u1q]

Thank you

[@guersomfalcon7544]

1:11 But order of operations tells we have to do the multiplication before subtraction.

[@ProfessorDaveExplains]

there is no multiplication present, 3x is a single term that can't be simplified. the PEMDAS stuff is pretty elementary school, it's not really going to come up anymore moving forward.

[@davidashu3626]

Hello professor Dave, when you multiplied both side by four, you said the 4 at the denominator at the right side cancels the 4 that was used to multiply it, pls I want to know if that 4 actually canceled the parenthesis that covered (3 - 3x)as well Thank you very much sir.

[@AnatoliiSkidchenko]

David should be rewarded with Nobel prize

[@technosoid2821]

Thank you so much Dave.

[@bilkis683]

I’m year four and you made it look easy and I told my teacher to tell me algebra and he told me hard ones like 12x=156 which is 13 and 6x+4=46 which is 7

[@moupiyasawoo1504]

Thank you 🙏

[@randomaccount2685]

4:50 Why are you subtracting the 12 instead of the 3?

[@keviherr]

So he can get rid of the 12 which is in the same side of 27x. Remember, our goal is to get X all alone.

[@bjornekholmeriksson5080]

Professor at 75% speed: We will later see plenty of examples that require much more manipulation than this Me at 200% brain gymnastics: 😑

[@yeshaalmanon1984]

one down, thanks chitcher!

[@foxvalorein9376]

At 3:33 you distribute a 3 - coincidence?

[@Silbeso]

3:36 why would you get 6x + 3????

[@nyxeanaaa12]

Basically.. 3.2x =6x (3.2=6 and then you just add the x cuz Its apart of it and we cant just skip it) then we add the + and then on the other side it's 3.1=3 So there it is 6x + 3

[@dhruvdodia1791]

Thank you❤️🙏

[@KebabEater]

How do you calculate (7x - 7)/3 =14? As in the steps? i don't know why but it has confused me.

[@reaupagatpatan7612]

Multiply 14 by three to get 42 then add 7 to get 49 then divide by 7 to get 7

[@KebabEater]

@@reaupagatpatan7612 Hey thanks, i figured it out lol

[@reaupagatpatan7612]

@@KebabEater I subscribed you

[@KebabEater]

@@reaupagatpatan7612 Thank you but there's no need i don't make any videos.

[@amanvalodia3669]

@@reaupagatpatan7612 thank

[@teacher.prashantdubeyforma5142]

very good presentation there and good video. explanation cud be a little better in my opinion. thumbs up :)

[@zeroblue5599]

Blessing you prof

[@alyxkrieger6764]

I like to use practice sheets as a 'warm-up' before continuing.

[@Kor491]

This guy's intro is keeping me sane

[@amchedli]

Hey Prof. Dave, I get a little confused at 2:08. When combining the like terms 4x and x, are we assuming that x is the same as 1x? thanks

[@amchedli]

Also, at 4:46, why does 3x on the left side of the equation cancel out? shouldn't it become 6x? Thanks

[@ProfessorDaveExplains]

yes, x is the same as 1x! and at 4:46, we have minus 3x, so adding 3x cancels it out. it's like - 3 + 3, just with algebraic terms!

[@amchedli]

Thank you!!

[@shoneappuhamy5165]

Professor, I could not understand how to evaluate the last two questions in Checking Comprehension, can you explain how to evaluate that, please!

[@saitama22]

(7x-7)/3=14 multiply 3 to both sides (7x-7)/3 * 3 = 14 * 3 which becomes, (7x-7) = 42 now remove the brackets, 7x - 7 = 42 add 7 to both sides 7x - 7 + 7 = 42 + 7 which simplifies to 7x = 49 now, divide both sides by 7 7x/7 = 49/7 which inturn simplifies to x = 7

[@kugaththeplaguefather6332]

5:55 how did Prof. Dave get x=7 from number 3

[@fredstead5652]

Same issue man. I know this is a year ago, but any chance you could still shed some light? It's a simple problem but I feel like I'm missing a core step

[@fof3904]

I didnt what combine means? In 2:00 why the equation turn from 4X TO 3X?

[@ProfessorDaveExplains]

so if you have 4 x's, and you subtract 1 x, you have 3 left over. Think of x's as something else, like apples.

[@chourouk-gr9qg]

I love solving equations man

[@GamerSaga]

hello, with the 3 -3x / 4 and dragging it over to multiply is it similar to how you let say change a negative to a positive. but in this cause change a division to multiple?

[@ProfessorDaveExplains]

sure, that's a good way to look at it!

[@TheKids422]

Dave should be awarded as the top iq.

[@CornerSlash]

Can someone explain the answer for question 2 in the comprehension check? 2(x+6) = 4(x+1)

[@heidysilva.4428]

I need to knowwwwwwwwwwwwwwwwww. help.

[@fredstead5652]

I understand you've likely already solved the problem, but I'm going to leave this here in case anyone else may need it. The operations go like this: The first operation is 2 times (x + 6). 2 times x is 2x and 2 times 6 is 12, this leaves us with 2x + 12. You now do the same to the second side of the equation, 4 times (x + 1). 4 times x is 4x, 4 times 1 is 4. This leaves us with 2x + 12 = 4x + 4. You're can now to merge the X terms. 4x - 2x is 2x, leaving us with 12 = 2x + 4. Subtract 4 from both sides to leave us with 8 = 2x. Finally, divide 8 by 2 (the inverse of multiplication) and you've got your answer. Hopes this helps anyone struggling.

[@launar463]

@@fredstead5652 thank you! I was so lost

[@deathisourgift]

I keep on finding "x = 5" to the third equation (instead of 7)... Can someone help me figure it out?

[@ProfessorDaveExplains]

hmm, i'm not sure exactly how you're going about it, but you should first multiply both sides by 3 to get 7x - 7 = 42. then add 7 to both sides to get 7x = 49. then divide both sides by 7 to get x = 7

[@deathisourgift]

THANK YOU! I actually subtracted 7 instead of adding it to 42... Beginner's mistake :/ Thanks a lot for these videos!

[@Sam-nm6nk]

@@deathisourgift I did the exact same thing, glad you asked the question.

[@davidashu3626]

Hello professor Dave, when you multiplied both side by four, you said the 4 at the denominator at the right side cancels the 4 that was used to multiply it, pls I want to know if that 4 actually canceled the parenthesis that covered (3 - 3x)as well Thank you very much sir.

[@revecacristina619]

Yes It does Its transfered not put

[@wongkinhang28]

♾️ Respect

[@bilkis683]

I don’t get this episode

[@rllrll9512]

Tell me plz , if i have an equation in which both sides with different variable and the relation on both sides is multiplication only(no add, subtract) ?????

[@ProfessorDaveExplains]

depends on the equation! you can email me an example if you like.

[@UseHerName000]

thank youu

[@johnmerllbaxinela478]

My PTSD has returned.

[@JoelMcCary]

Bro what do you mean x -x is 0 but if there's a 4x -x it gets to just say nuh uh?

[@sgript]

Think of x like apples. 4 apples minus an apple leaves you 3 apples (3x) One apple minus another apple leaves no apples (0x, hence no x)

[@wafualex7930]

in india we do the dragging thing for addition n subtraction too and it's way easier

[@oshiezz]

so usually its PEMDAS but for algebra its SADMEP?

[@florencenn9557]

Great video. In the last sum i got -x=16.... In one of your example sums when x was negative you said that we had to find the value of positive x..So does that mean that to get the correct answer , 16 and -x switch sides? I didnt really understand that part.

[@ProfessorDaveExplains]

just multiply both sides by -1, and you get x = -16!

[@florencenn9557]

Oh I understand now. Thank you!

[@pobletekinze6537]

3x-2=5x+8 -2=8x+8 8x=-10 x= -4/5 2(x+6)=4(x+1) 2x+12=4x+4 12=2x+4 8=2x 4=x (7x-7)/3=14 7x-7=42 7x=49 x=7 (5x-4)/3=2(x+2) 5x-4=6x+12 -4=x+12 x=-16

[@pobletekinze6537]

3x-2=5x+8 -2=2x+8 -10=2x x=-5

[@professorelixir3351]

@@pobletekinze6537 Right

[@davidashu3626]

And also professor Dave, how are you able to reduce -9/27 to -1/3?

[@ProfessorDaveExplains]

divide top and bottom by 9!

[@KamogeloSlater]

For question 2 isn't the answer 5

[@sislol3685]

When you flip the number to the other side of the equal, you have to change the sign right?

[@ProfessorDaveExplains]

yep

[@sislol3685]

@@ProfessorDaveExplains Thanks for the answer

[@34kylerozario54]

2:00

[@adrianclark2734]

hi @professor Dave Explains. I am having more trouble than I ought to be here. So I'm following the steps you've laid out for Q4 on the comprehension part, but it's totally failing me. I'll show you my steps. (5x-4)/3=2(x+2) that should lead me to: 5x-4=(2x+4)3 this gets me to: 5x-4=6x+12 right? Then I go ahead and add 5x to both sides and things get weird when i get to the answer, I feel like this is where I'm going wrong. But I'll continue. 5x+5x-4=6x+5x+12 = -4=11x+12 I then minus 12 from both sides. -12=11x I then swap these around and divide them both by 11x (11x=-12) x=1.090909090909??? Seriously, this is screwing with me :'D I'm clearly making a dumb mistake, please can you help me?

[@marithmae]

You actually had everything correct up until you added 5x to both sides. What actually needs to happen is that 5x needs to be subtracted from both sides. At that point you would get - 4 = x + 12. The final step would be to subtract 12 from both sides to isolate the variable, and you wind up with x = -16. Hope this helps!

[@adrianclark2734]

@@marithmae thank you so much, I have no idea what made me the 5x instead of subtracting

[@kugaththeplaguefather6332]

can anyone show me how he did the solutions in 5:55 on all question

[@padmamamidwar9536]

Hey bro Just work smart go on google lens and click on homework Then click a picture of the problem and you will get the steps and answer

[@ridmicmeena4123]

@ProfessorDaveExplain plz help me with the last equation - (5x - 4)/3 = 2(x+2) plzzzz anyone can ????

[@carl8790]

I'll take a shot; first distribute 2(x+2), you'll get 2x+4. Secondly, to get rid of the /3 in (5x-4)/3, multiple by 3 in both sides. Eventually, you should get 5x-4 = 3(2x+4). Thirdly, distribute 3(2x+4), you should get 6x+12. Then combine all the x variables on the left or right side, and do the same for the numbers. I have it as 5x-5x-4 = 6x-5x+12, calculate and it should be -4 = x+12, which can also be written as x+12 = -4. For the numbers, do the same, x+12-12 = -4-12, calculate; answer is x = -16. Hope this helps!

[@jcas2083]

How did you get -16 and not positive 16 for the last one?

[@TherealYUVRAJ]

5x - 6x = 12 + 4 -x = 16 x = -16

[@joansilvania9000]

Im stuck at the bottom right equation at the end of the vid.. idk how to solve it

[@emaobono]

Please sir where can we get more comprehension

[@davidcalderon6062]

Why does 4x-x=3x? shouldn't x-x lower the multiplicand not the multiplier?

[@ProfessorDaveExplains]

Think about it as four apples minus one apple.

[@davidcalderon6062]

@@ProfessorDaveExplains I got it now I read elsewhere when subtracting the variable from the term it is equivalent to subtracting a like term with a 1 so 4x-x =3x can be read as 4x - 1x = 3x. Thank you for your videos truly an amazing job.

[@rj4789]

Need more examples to practice

[@Xstreamster]

Can someone explain to me how on the third equation with 7x - 7/3 = 14, x= 7, becuase i always get the answer to 5

[@TherealYUVRAJ]

7x - 7 = 14 * 3 7x - 7 = 42 7x = 42 + 7 7x = 49 x = 49/7 x = 7

[@aminmkyt4191]

I felt in love with algebra, you had to be a dating coach

[@duulga1290]

Professor dave what if we had 3x-7=16 or something like that How would u do it?

[@NexushasTaken]

3x-7=16 3x=16-7 3x=9 (3x)/3=9/3 x=3

[@jazzyj577]

Need help with statistics

[@ValiantViper123]

In comprehension section, (7x-7)/3 = 14, the answer is written wrong. It should be x = 5;

[@TherealYUVRAJ]

bro you need to add 7 in 42 = 49 then divide it by 7 which will give you 7

[@TherealYUVRAJ]

7x - 7 = 14 * 3 7x - 7 = 42 7x = 42 + 7 7x = 49 x = 49/7 x = 7

[@precisioninc4870]

That last problem was hard to try to do in your head while eating xD

[@fei_073]

My answer for no. 3 was wrong, which is 5. Please explain how it turned out to be 7.

[@TherealYUVRAJ]

7x - 7 = 14 * 3 7x - 7 = 42 7x = 42 + 7 7x = 49 x = 49/7 x = 7

[@michaelfuxeklint4909]

An apple a day, keeps the doctor away 😏😏

[@ashwinchester6594]

I'm so confused by all of the comprehension questions. Would someone mind walking me through how to get the answers?

[@JoelMcCary]

Im falling asleep watching this💀💀💀💀

[@harrymatabal8448]

x=-3

[@gosifefavour6111]

we call that cross multiply

[@JoelMcCary]

How does 3x-2=5x+8 = x=-5

[@gigachad-vv8ev]

up

[@rayenamarir5764]

Same question

[@Mamadvali-02]

❤❤❤

[@qiwamiz]

This is a great video but why do you have to divide and subtract with only 3? Is there some kind of thing that you use to get that number

[@carultch]

It's just a coincidence that the two examples he made up, worked out that way. The number 3 is the coefficient on x, in both examples, so in order to isolate x and make x the subject, we need to divide the equation by 3. If the example at 1:46, were instead given as 7*x + 3 = x - 6, then you wouldn't divide by 3. Here's how you'd solve it: 7*x + 3 = x - 6 Subtract 3 from both sides, and simplify: 7*x = x - 6 - 3 7*x = x - 9 Subtract x from both sides and simplify: 7*x - x = -9 6*x = -9 Divide by 6: x = -9/6 Simplify and get our solution: x = -3/2

[@IsaPat]

≈∞

[@subhrapratimsharma2825]

The views are gradually decreasing.

[@ProfessorDaveExplains]

huh?