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Solve for x 5/3 = 1/2(x^-1)(y)

  1. Jan 25, 2013 #1

    939

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    1. The problem statement, all variables and given/known data

    Solve for x. I know how to do this when there is addition and subtraction but I'm confused what to do when there is multiplication. Sorry for the newb question...

    2. Relevant equations

    5/3 = 1/2(x^-1)(y)

    3. The attempt at a solution

    10/3 = (x^-1)(y)
    (10/3)/(y) = (x^-1)
     
    Last edited: Jan 25, 2013
  2. jcsd
  3. Jan 25, 2013 #2

    Mark44

    Staff: Mentor

    Is this 5/3 = 1/2 * x-1 * y?

    If so, for starters, multiply both sides of the equation by x.
     
  4. Jan 25, 2013 #3

    939

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    Yes, it is, sorry...

    5/3(x) = (1/2)*(y)
    then... divide both sides by 5/3?

    x = 3/10(y)
     
    Last edited: Jan 25, 2013
  5. Jan 25, 2013 #4

    Mark44

    Staff: Mentor

    Right, but this would be clearer as 3y/10.
    If you write it as you did, some might (mistakenly) think you meant 3/[10y].

    Also, dividing by 5/3 is the same as multiplying by 3/5, the reciprocal of 5/3.
     
  6. Jan 25, 2013 #5

    939

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    Got it. Thanks yet again.
     
  7. Jan 25, 2013 #6
    You are trying to solve for x so my approach would be to solve to y in terms of x and then plug that into y so there is only x in the equation and then solve for x, so

    5/3 = 1/2 * x^-1 * y
    Multiply both sides by x as you did before
    5/3x = 1/2 * y
    Divide both sides by 1/2
    10/3x = y

    Now plug that into the original equation for y and then solve for x.

    5/3 = 1/2 * x^-1 * (10/3x)

    Solve for x. If my math is wrong please correct me, it's been some time since I done a problem like this.
     
  8. Jan 25, 2013 #7

    tms

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    Do that and you'll find that 5/3 = 5/3.
     
  9. Jan 26, 2013 #8

    Mark44

    Staff: Mentor

    Since the instructions are to solve for x, it's a waste of time to solve for y first. All you need to do is get rid of the 5/3 coefficient of x, which you can do by multiplying both sides by 3/5. This leaves you with x = 3y/10, as before.
     
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