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B Confusion over transposing formulae question

  1. Nov 14, 2016 #1
    Hello I'm working through transposing formulae of pearsons Anthony Croft and Robert Davidson's foundation maths 5th edition and I'm stuck on exercise 10.1 question 1)e)
    We're it states that I must transpose the formula to make x the subject.
    The formula is y = ¹/₂x and the answer x = ¹/₂y
    I don't understand how they got this answer. As I did the working as
    E)y = 1/2x
    × 2
    (2)(y) = ⁽¹⁾/₍₂₎x × ⁽²⁾/₍₁₎
    2y = x
    I base this way of a working off another question which I got correct
    D)y = (¹)/(₂)(x - 7)
    + 7
    y + 7 = ¹/₂x
    × 2
    (2)(y + 7) = ⁽¹⁾/₍₂₎x × ⁽²⁾/₍₁₎
    2y + 14 = x
    x = 2y + 14
    If I am missing some rule that I'm meant to implement or if there is a error in the textbook your advise would be greatly appreciated.
    Yours sincerely Buggsy
     
  2. jcsd
  3. Nov 14, 2016 #2

    mfb

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    That is correct.
    That step is incorrect at the right side.

    Try x=7 and see if you can find a value for y such that both the initial and the final formula are right.
    That does not make sense.
     
  4. Nov 14, 2016 #3

    PeroK

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    If ##y = \frac{1}{2x}## then ##x = \frac{1}{2y}## is correct.

    Try ##x = 1## for example.
     
  5. Nov 14, 2016 #4

    mfb

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    I didn't expect x and y to be in the denominator.
     
  6. Nov 14, 2016 #5
    I know but look
    IMG_1479155097.809314.jpg IMG_1479155113.861736.jpg
     
  7. Nov 14, 2016 #6
    Pardon me Perok can you take a picture of your working and post it, for some reason your post shows up on my screen as a bunch of hashtags and letters.
    Thank you
     
  8. Nov 14, 2016 #7

    PeroK

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    I'm sorry to tell you I did it in my head!
     
  9. Nov 14, 2016 #8

    PeroK

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    Hint: multiply by ##x## to start.
     
  10. Nov 14, 2016 #9
    So it look like this View attachment 108916
    Ok second question how did you know to start with x not to just repeat the same action I used to get rid of the 1/2x in question d)
    We're the answer was x =2y + 14 were the original formula was y = ¹/₂x - 7
     
  11. Nov 14, 2016 #10

    PeroK

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    That last equation is very different. That is

    ##y = \frac{x}{2} - 7##
     
  12. Nov 14, 2016 #11
    I'm sorry this taking a while but can tell me is there a rule I should remember or an order of operation when rearranging formulas as I' m getting different answers depending on how I start to balance the equation even if I balance both sides all the way through
     
  13. Nov 15, 2016 #12

    Mark44

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  14. Nov 15, 2016 #13
    Question e) and d) 10.1
     
  15. Nov 15, 2016 #14

    PeroK

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    That simply means you are making a mistake. There are no rules except you can: a) add the same thing to both sides of the equation; or, b) multiply both sides of the equation by the same thing. That same thing can be a number, such as ##2## a parameter, such as ##a##, or a variable, such as ##x##.

    For example:

    ##y = ax + b##

    ##y-b = ax## (added ##-b## to both sides, which is the same thing as subtracting ##b##)

    ##\frac{y-b}{a} = x## (multiplied both sides by ##\frac{1}{a}##, which is the same as dividing by ##a##)

    Another example is:

    ##y = \frac{1}{x}##

    ##xy = 1## (muliplied both sides by ##x##)

    ##x = \frac{1}{y}## (divided both sides by ##y##)
     
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