Rearranging Equations

38 Responses

  1. Leon dunn says:

    Thankyou for all the help on this but im still slightly confused on what you do if you have a more basic one like this x/2=a and you have to rearrange to make x the subject. please help my teacher didnt explain it very well.

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    • admin says:

      This is a good method to use when rearranging fractions. I assume the question is arranged as below;

      a is the same as a/1, So you rewrite it like this. I hope you realise why.

      You then “cross multiply”. You multiply x with 1 and 2 with a.

      This leaves;

      It does not matter if 2a comes first or x comes first. It is the same.

      Like or Dislike: Thumb up 24 Thumb down 2

      • Sam Dickinson says:

        Is it always possible to rearrange an equation to get one term? In physics we have the equation of motion s=ut+1/2at^2. I can’t see how to rearrange that to describe t in terms of u, a and s.

        Like or Dislike: Thumb up 3 Thumb down 0

  2. Ben says:

    break it down on how to solve for Q

    5,967=[Q(3-0.3)-40,000](.85)+(4,000x.15)

    Thanks you =)

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  3. najma says:

    what if you have y=a/(x+b)2 making x the subject

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    • corano says:

      to type squared, di it like this x^2
      multiply both sides by (x+b)^2
      y*(x+b)^2=a
      then divide both sides by y
      (x+b)^2=a/y
      square root both sides to get rid of the squared
      x+b= root(a/y)
      subtract b from both sides
      x=root(a/y)-b

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  4. Lucy says:

    I still find it VERY confusing! :-(

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  5. Melissa says:

    HELP :
    B = U(N)(I) / L
    Need to find U

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  6. lucy hartley says:

    how do u rearrange the equation y=4(3+x) to make x the subject??

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    • Author says:

      Hello Lucy,

      I will answer that for you. First you will need to expand the expressions so you get;
      \[ y = 12 + 4x \]
      Move 12 to the left hand side to get;
      \[ y - 12 = 4x \]
      The divide both sides by 4 to get;
      \[ \frac{y - 12}{4} = x \]
      It does not matter if x comes first because it is the same;
      \[ x = \frac{y - 12}{4} \]

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  7. Pedro Garcia says:

    p= sqaureroot(1-m2)/m
    m=?

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  8. Ginger says:

    How do i rearrange 4x = 8x-2/3 to make x the subhect??

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    • Ed says:

      a bit late to the party, but it’s very simple – what you do to one side, you have to do to the other. In this case, 4x = 8x-2/3

      1. multiply both sides by 3 to remove the fraction

      12x = 8x-2

      2. you can now minus 8x from both sides so it will become:

      4x = -2

      I’ll let you figure out the rest ;)

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  9. Rebecca says:

    0.17 = x + 2.4 (0.1 – x)

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    • Helen says:

      Hi Rebecca,
      I am not sure if you have received the answer to your problem, but this is how I would have done it. 0.17=x+2.4(0.1-x)
      1) take the last part 2.4(0.1-x) and multiply everything in the bracket with 2.4 you have;
      \[ 2.4 × 0.1- 2.4x = 0.24 -2.4x \]
      2) Then you put it back in your formula;
      So you have;
      \[ 0.17 = x + 0.24 - 2.4x \]
      3) Then what I did, you collect all the terms with X;
      so you have
      \[ x - 2.4x =- 1.4x \]
      4) Then I had \[ 0.17 = 0.24 - 1.4x \]
      5) Then you move those nu without X from right to left but remember to change the sign to a negative as 0.24 is on the right positive, you will have ;
      \[ 0.17 - 0.24 = - 1.4x \]
      6) Then you divide both sides by 1.4 and you are left with the fraction as 1.4 ÷ 1.4 X will be cancelled and you are left with X. So you are left with X = 0.17 -0.25 ÷ 1.4. Remember this is a fraction after the equal. I am having trouble with the keyboard, doesn’t have fraction on my tab. Hopefully it is correct but that was my logic in solving that . What is yours? Maybe I am wrong, maybe you get a better answer,let me know. Bye,good luck.

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  10. joel says:

    Rearrange the following equation to find x in terms of a and b, in
    simplest form (assume that a ‘= 4b):
    a(a − x) + 4b(x − 4b) = 0.

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    • Author says:

      You have to try otherwise you may not get any reply. I also think you have written the question wrong. I will start you off.
      If we have to write the new expression in terms of a and b then we won’t need this “Assume that a = 4b” because we have to include a and b in the final expression when x is the subject. So I will ignore that. We’re starting with;
      \[ a(a - x) + 4b(x - 4b) = 0 \]
      First will need to get rid of the factors ( expand the expression ).
      \[ a^2 - ax + 4bx - 16b^2 = 0 \]
      We collect like terms and make sure that all terms that contain x are on one side.
      \[ -ax + 4bx = 16b^2 - a^2 \]
      You should be able to finish off from here.

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  11. unknown says:

    h=bx-a/c

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  12. unknown says:

    what is ch=bx-a

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  13. Author says:

    What are you trying to find?

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  14. sean says:

    Hello. 22/m = 9 + m. how would I go about finding m?

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    • Author says:

      Hello Sean,

      You have to show that you tried, so that we know where you’re stuck. I assume you have the expression as;
      \[ \frac{22}{m} = 9 + m \]
      I will help you get started. We must have m on its own on one side. To get rid of m on one side we must multiply both sides by m. Notice that if you do so you’ll have to divide the ms in the fraction side. Or you could use the cross multiply technique described above. When you do this you will get;
      \[ 22 = m(9 + m) \]
      It is very easy to continue from here.

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  15. Peter says:

    Hi how would i go about rearranging this?To find x “0=5x^4+3x^-4″

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  16. Charlie says:

    Hello Great Site… This helped me alot. But i still don’t understand the rules of like ‘negative or positive’. I have this sum “F=mg-kv^2″ make v the subject… I keep getting answers like this… sqrt(60*250/-0.1*10)… I know the answer but have no clue how to properly do this question.
    Thankyou so much
    Charlie

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    • Ed Jones says:

      Hello Great Site… This helped me alot. But i still don’t understand the rules of like ‘negative or positive’. I have this sum “F=mg-kv^2″ make v the subject… I keep getting answers like this… sqrt(60*250/-0.1*10)… I know the answer but have no clue how to properly do this question.
      1) Add kv^2 to both sides to get F+kv^2=mg
      2)Take F for kv^2 = mg-F
      3) Divide by k for v^2 = (mg-F)/k
      4) Square root to get:

      v = sqrt((mg-F)/k)

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    • Ed Jones says:

      1) Add kv^2 to both sides to get F+kv^2=mg
      2)Take F for kv^2 = mg-F
      3) Divide by k for v^2 = (mg-F)/k
      4) Square root to get:

      v = sqrt((mg-F)/k)

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  17. Kadiesha says:

    Helpful site.. though how do you rearrange A=(a+b/2)h so that a is the subject? Any help would be so so appreciated. Thanks!

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  18. ali says:

    how would you rearrange this
    vo = (v2-v1)rf/r1
    to make v2 the subject

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  19. Av says:

    Thanks very much for sharing your knowledge!! it has made maths simpler!!

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  20. Aimee says:

    Hey, this has been really helpful but I’m a bit confused; how come in the question in the comments y=4(3+x) do you expand the brackets but not in the example x=k(y+z)

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  21. Nathan says:

    hey, I’ve had mixed information on how to rearrange this equation

    a=b/4-c

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    • Sam Dickinson says:

      To find ‘b’ or find ‘c’? And is that ‘(b/4)-c’ or ‘b/(4-c)’?

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    • Ed Jones says:

      If you want to rearrange for b:
      Add c to both sides to get a+c=b/4
      Times both sides by 4 to get either b = 4(a+c) or b = 4a + 4c

      For c:
      Add c to both sides to get a+c = b/4
      Take away a from both sides to get c = b/4-a

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  22. + says:

    Grammar error.
    In the third line.

    Well done.

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  23. When simplifying indicies how would you do (mn^-2)4?
    And how would u make a and then d the subject of this formula: s=n/2(2a+d(n-1)?
    Many thanks!

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  24. Ameena says:

    What about a(x+1)=b(x+2)

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