David Wright
David Wright
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Rearrange to make x the subject
Change the subject of equations by learning how to rearrange for x and y and other variables. GCSE | IGCSE (Higher Tier).
Transcript:
Hi everyone and welcome to my channel.
In this video I’m going to give you a step-by-step guide about how to answer questions that ask you to rearrange equations in order to change the subject.
In this question we are given an equation where y is the subject (note that this means it is on its own on the left), and we are asked to make x the subject, which is currently part of a more complicated expression on the right.
So what we are going to learn how to do is to take the y variable over here on the left and move it over to the right-hand side of the equation.
And we’re also going to learn how to move the x variable on the right over to the left-hand side and rearrange the equation so that it is on its own and is therefore the subject of the equation.
This question is well worth studying for GCSE because it’s very typical of the type of question you may be asked.
This is because the exam questions often contain a square root, like we have here and so it’s very important that you understand what I am going to show you next.
This is because we need to get rid of the square root in order to make x the subject.
And the way that we do that is to square both sides of the equation.
What this means is that we multiply each side by itself.
So on the left we have y times y, which is y-squared
And on the right, one times one is 1-squared.
This is just one, so we don’t need to change this.
But, more importantly, we have the square root of x+2, which is then squared.
This is a maths technique to get rid of the square root, and it simplifies to just x+2.
You can check this effect by multiplying any square root by itself.
So if we take the square root of 2 and multiply it by the square root of 2, which can is also written as the square root of 2 squared, then the answer is 2.
It works for any number, so the squaring technique is simply a way of removing square root signs to make our equation simpler.
So that’s the first step we need to do to change the subject of our equation.
I’ll put what we started with over here on the right and we can then see how it changes after each step.
And the next step is to multiply both sides by x+2. And the reason for doing this is that it has the effect of moving this x+2 over to the left-hand side, which is what we want to do.
So we multiply the left-hand side by x+2, and then we do the same to the right-hand side.
This step is also important because this x+2 and this x+2 cancel each other out, leaving just the number 1 on its own on the right-hand side.
So, it’s now starting to look simpler, and we need to find a way of moving this y-squared, and this plus 2, over to the right-hand side.
And we do this by firstly dividing both sides by y-squared.
In a similar way to the step above, y-squared divided by y-squared cancels, leaving just x+2, and on the right we get 1 divided by y-squared, which is written as 1 over y-squared.
So we’re almost there.
All we need to do next is subtract 2 from both sides.
So on the left, 2 minus 2 cancels, leaving x on its own.
And on the right we have 1 over y-squared minus 2.
And so we’ve arrived at our answer.
We started with this.
And by applying some important algebra techniques we were able to rearrange to change the subject to x.
I hope that this video has helped you, and that you understand the steps I have shown.
Please Subscribe, Like and Share to help my channel to grow, and leave a comment if you need help with this type of question.
Many thanks for your interest in maths and I wish you all this best.
Переглядів: 1 656

Відео

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Переглядів 1982 роки тому
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КОМЕНТАРІ

  • @rakhiskitchen3328
    @rakhiskitchen3328 2 дні тому

    Can u pls tell what if the equal to value also has a negative base? Kindly tell

  • @elizabethconcepcion2151
    @elizabethconcepcion2151 8 днів тому

    Thank you ever knew

  • @MUZANGALUMUNZENZI
    @MUZANGALUMUNZENZI 12 днів тому

    Y can't you reduce the words on the screen ,we easily get obstructed.

  • @ShoaibKhan-wx8sn
    @ShoaibKhan-wx8sn 29 днів тому

    I have this same calculator but the problem is I dont know how use its functions like those on the mode menu. Can you guide me? And also where is the matrix option in this couldn't find it

  • @SamiuelaMakaafi
    @SamiuelaMakaafi Місяць тому

    Not me watching this 2 hours before my math exam

  • @11KNOCKOUT
    @11KNOCKOUT Місяць тому

    👏👏👏👏👏👏👏👏🌹

  • @jameeltarekTarek
    @jameeltarekTarek 2 місяці тому

    Thank u w❤❤❤❤❤❤❤

  • @bobbu95
    @bobbu95 2 місяці тому

    Thank you very much. Clear and concise explaination. Cheers!

    • @DavidWrightUK
      @DavidWrightUK 2 місяці тому

      No problem. Glad the video helped👍

  • @Someguyagain
    @Someguyagain 2 місяці тому

    Using this in my college exams

    • @DavidWrightUK
      @DavidWrightUK 2 місяці тому

      Best of luck. Hope the video helps 👍

  • @dathrangkiopakyntein5000
    @dathrangkiopakyntein5000 2 місяці тому

    Thanks🙏

  • @hamsterelephant2055
    @hamsterelephant2055 2 місяці тому

    Thank you!!! As an IG student i found your videos very very helpful! Pleases keep going with this channel❤❤

    • @DavidWrightUK
      @DavidWrightUK 2 місяці тому

      Thank you for leaving such a nice comment. I appreciate it and plan to start making videos again in the autumn. I hope your studies go well and wish you all the best.

  • @benjaminmaurice9740
    @benjaminmaurice9740 2 місяці тому

    The Cos -π/4 didn't give me 2 so how'd you get yours??

    • @DavidWrightUK
      @DavidWrightUK 2 місяці тому

      You have to make sure your calculator is set in radians. You also might be getting an answer that is equivalent. For example 1/sqrt(2) is the same as sqrt(2)/2.

  • @crystalcoleman7343
    @crystalcoleman7343 2 місяці тому

    What do you do if they don’t give you all the values

    • @DavidWrightUK
      @DavidWrightUK 2 місяці тому

      The question should give a clue about what the total should be.

  • @yogendramishra1125
    @yogendramishra1125 2 місяці тому

    thank u very much Guruji for the video ❤

    • @DavidWrightUK
      @DavidWrightUK 2 місяці тому

      No problem. Glad I could help 😃

  • @CocoCutiePie
    @CocoCutiePie 2 місяці тому

    watching this while omw to exam hall

  • @chibangatryson6379
    @chibangatryson6379 2 місяці тому

    Thanks 👍👍🙏🙏

  • @shariqkhan8181
    @shariqkhan8181 3 місяці тому

    Thank you

  • @travler2899
    @travler2899 3 місяці тому

    Fx991es?

    • @DavidWrightUK
      @DavidWrightUK 3 місяці тому

      Unfortunately there isn't a factorial button on this model.

  • @travler2899
    @travler2899 3 місяці тому

    I have fx991es plus 😢

    • @DavidWrightUK
      @DavidWrightUK 3 місяці тому

      A few people have mentioned this before because the FX991ES doesn't seem to have the factorial function.

  • @mwanikaalex4931
    @mwanikaalex4931 3 місяці тому

    Voice is blurred

  • @Black.Switch
    @Black.Switch 3 місяці тому

    Thank's Davied I appreciate it so much

    • @DavidWrightUK
      @DavidWrightUK 3 місяці тому

      No problem. Best of luck with your studies.

  • @NathanVillanuevaBC
    @NathanVillanuevaBC 3 місяці тому

    Aren't you to add 2π to -π/4? I've solved it differently and this is my result: Z = 2sqrt(2) (cos(7π/4) + isin(7π/4))

    • @DavidWrightUK
      @DavidWrightUK 3 місяці тому

      The two answers are equivalent because the difference is 2*pi as you've mentioned. Some university courses want an answer between 0 and 2 pi, whilst others want answers from 0 to pi / 0 to minus pi. There isn't a standard convention for this which is why sometimes you will get different (but equivalent) answers in this type of problem.

  • @maamenyene8035
    @maamenyene8035 3 місяці тому

    this advice is abselutley garbage its shit

  • @ClaudiaJanuary-mu7ii
    @ClaudiaJanuary-mu7ii 3 місяці тому

    What if the equation is like X plus A equal X plus B divided by C change the subject to X

    • @DavidWrightUK
      @DavidWrightUK 3 місяці тому

      Try splitting the right-hand side into two fractions. Then apply the ideas shown in the video.

  • @vandanathomas658
    @vandanathomas658 3 місяці тому

    U explained it very nicely .Thank u very much .

    • @DavidWrightUK
      @DavidWrightUK 3 місяці тому

      No problem. I'm glad the video helped 😃

  • @charlesokuom8747
    @charlesokuom8747 3 місяці тому

    Well explained

  • @AayushPoddar-st3zn
    @AayushPoddar-st3zn 3 місяці тому

    why did '3y/2' changed to '3/2*y'?

    • @DavidWrightUK
      @DavidWrightUK 3 місяці тому

      3y means 3*y. Therefore 3y/2 is the same as 3/2*y. You can test this on your calculator. For example, if y=4 then (3*4)/2=6 and (3/2)*4=6. Hope this helps.

  • @arinzeanthony7447
    @arinzeanthony7447 3 місяці тому

    Do we use general argument when finding polar equivalent or is it a must or a standard to use principal arguments?

    • @DavidWrightUK
      @DavidWrightUK 3 місяці тому

      It is standard to use the principle argument which is the fraction in it's lowest form. For example, cos(pi/4) is the same as cos(9pi/4) and cos( 17pi/4) etc, the only difference is that 2*pi has been added to take account of one revolution around the unit circle. However your teacher might be asking you to consider the odd and even nature of sine and cosine functions. For example cos(pi/4) is the same as cos(minus pi/4), which is also the same as cos (7pi/4). I would need to make a separate video to cover this but you can find out more information if you research the properties of the unit circle.

    • @arinzeanthony7447
      @arinzeanthony7447 3 місяці тому

      @@DavidWrightUK ohh. I now understand. Thanks a lot.

  • @goatlps
    @goatlps 4 місяці тому

    0:28 It's quicker to just put in .2 x 115. Is there a way to calculate "50% more" without doing (.5 x 115) + 115 = 172.5? Apart from 1.5 x 115, obviously.

    • @DavidWrightUK
      @DavidWrightUK 4 місяці тому

      1.5 x 115 is pretty quick on a calculator. If you are doing the calculation in your head then you could add on 50% of 100 first, giving 150. Then add on 50% of 15, giving 22.5. The total is therefore 172.5.

  • @danielkelsosmith
    @danielkelsosmith 4 місяці тому

    Why have we gone in a negative direction? That’s what I’m failing to understand. If we are working in the 3rd and 4th quadrant are we going in a negative direction?

    • @danielkelsosmith
      @danielkelsosmith 4 місяці тому

      And how would you do one in the third quadrant?

    • @DavidWrightUK
      @DavidWrightUK 4 місяці тому

      It is convention to regard the third and fourth quadrant as the negative direction so that none of the angles are more than plus or minus pi.

    • @danielkelsosmith
      @danielkelsosmith 4 місяці тому

      @@DavidWrightUK thank you. Lost sleep over this question haha

  • @SundaeOfDoom
    @SundaeOfDoom 4 місяці тому

    Thank you for explaining it so clearly!

    • @DavidWrightUK
      @DavidWrightUK 4 місяці тому

      You're welcome. I'm glad the video was helpful 😃

  • @phill12345
    @phill12345 4 місяці тому

    Thanks ❤❤❤ On point 📌

  • @kaymo7498
    @kaymo7498 4 місяці тому

    Wow i was in so much stress because i could not understand this polar form thing but you just made it so simple and easy to understand,thank for the work that your doing,God bless your brother.

    • @DavidWrightUK
      @DavidWrightUK 4 місяці тому

      I'm glad the video helped and wish you all the best with your studies 👍

  • @user-ze1en9nn8i
    @user-ze1en9nn8i 4 місяці тому

    We're nothing without you

  • @dgossymax
    @dgossymax 4 місяці тому

    Thanks mate you're a good lad

    • @DavidWrightUK
      @DavidWrightUK 4 місяці тому

      No problem. Glad I could help 👍

  • @mujiman182
    @mujiman182 5 місяців тому

    Who let him cook

  • @user-zt1em2ry5n
    @user-zt1em2ry5n 5 місяців тому

    Thank you morning before big test 3.51 am thank you 👌

    • @DavidWrightUK
      @DavidWrightUK 5 місяців тому

      That's a long night. Hope the test goes well 😀

  • @user-ju5xk9ek5k
    @user-ju5xk9ek5k 5 місяців тому

    My calculator doesn't have shift.😂

    • @susanallan-c4828
      @susanallan-c4828 3 місяці тому

      Mine doesn't either but that's because mine doesn't need shift to use the % sign. It's a simple calculator with everything on the one level. I presume here that the sophisticated calculator needs Shift like you use it typing on a computer keyboard. This video has been a real help to me. I could only do the calculation with pen and paper.

    • @DavidWrightUK
      @DavidWrightUK 3 місяці тому

      @@susanallan-c4828 Thank you for leaving a comment. When I made the calculator videos I didn't realise that there was such a wide variety of models that differ from country to country. I'm glad that the video helps for simple calculators with a % button. Percentages are not too bad after a bit of practice.

    • @user-di9mf3xf3k
      @user-di9mf3xf3k Місяць тому

      Then swift the calculater

  • @user-ti2hp6qq7p
    @user-ti2hp6qq7p 5 місяців тому

    Thank u a lot for the video

    • @DavidWrightUK
      @DavidWrightUK 5 місяців тому

      No problem. Good luck with your studies 😀

  • @miraclesamuel2235
    @miraclesamuel2235 5 місяців тому

    more explanation

  • @yangjeonginsgf
    @yangjeonginsgf 5 місяців тому

    Missed maths classes today, this helped a lot!

    • @DavidWrightUK
      @DavidWrightUK 5 місяців тому

      I'm glad the video was useful. Best of luck with your studies.

  • @sakshambhuwalka8184
    @sakshambhuwalka8184 5 місяців тому

    i suggest you make a videos upon solving a past igcse papers?

    • @DavidWrightUK
      @DavidWrightUK 4 місяці тому

      Thank you. I'll keep this in mind 👍

  • @tayshawnstrachan9078
    @tayshawnstrachan9078 5 місяців тому

    youtube be a life saver fr

  • @AmyLee-ci2sz
    @AmyLee-ci2sz 6 місяців тому

    I love u

  • @user-yu4sf8le4t
    @user-yu4sf8le4t 6 місяців тому

    ALIMOT FOLAKE. Thanks this really helps me with my homework

    • @DavidWrightUK
      @DavidWrightUK 6 місяців тому

      I'm pleased the video helped. Best of luck with your studies.

  • @user-yu4sf8le4t
    @user-yu4sf8le4t 6 місяців тому

    Sir you can make it❤😊

  • @matejavukovic6460
    @matejavukovic6460 6 місяців тому

    Do you know how to do it in a citezen sr-135N

    • @DavidWrightUK
      @DavidWrightUK 6 місяців тому

      Sorry I can't help but I've only used Casio calculators so don't know how to do it on other makes and models.

  • @bengom1279
    @bengom1279 6 місяців тому

    Why is iPhone calculator retarded?

  • @_.-Ava-._
    @_.-Ava-._ 6 місяців тому

    I'm stuck on a homework question which is asking me to make x the subject of y=(ax+b)/(cx) The part I don't understand is that there is a single positive x on both sides of the division, and based on what I've been taught in class this means x should cancel itself out. I've tried multiplying both sides by x, along with other attempts, but can't seem to rearrange the equation without x cancelling itself out. Not sure if you'll see this, but I thought I'd try because in the videos I've watched you've explained things in a very clear and engaging way. (Also sorry for the extremely wordy comment)

    • @DavidWrightUK
      @DavidWrightUK 6 місяців тому

      One way to simplify this question is to note that (ax+b)/(cx) = ax/cx + b/cx = a/c + b/cx . If you apply this simplication step the methods in the videos should help you find the answer. Hope this helps.

  • @user-os8qj7mw4r
    @user-os8qj7mw4r 6 місяців тому

    6/1/2024