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Homework Help: How do I solve an equation with a variable in the numerator?

  1. Sep 13, 2011 #1
    1. The problem statement, all variables and given/known data

    I just missed a 16-point question on a quiz because I didn't know how to separate the variable. It was an absolute value equation, but I just need to know how to deal with a variable in a fraction. Here's what it looked like:

    2. Relevant equations

    (5x+10)/2 = 20

    3. The attempt at a solution
    I tried multiplying everything by the denominator, but I'm not sure if or why that works. Any help would be greatly appreciated, thanks!
  2. jcsd
  3. Sep 13, 2011 #2


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    Staff: Mentor

    Multiplying by denominator should work. You can do anything that doesn't change the equality - that means adding, subtracting, multiplying or dividing both sides of the equation by the same thing.

    Or you could write the fraction as [itex]\frac {5x}{2} + \frac {10}{2}[/itex].
  4. Sep 13, 2011 #3
  5. Sep 16, 2011 #4


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    The easiest way is to multiply both sides of the equation by the denominator. The reason why this works is because it doesn't change the equality.

    (5x+10)/2 = 20
    5x+10 = 40
    5x = 30
    x = 6

    Even if the variable was in the denominator, you can still solve for the variable using the same steps.

    2/(5x+10) = 20
    2 = 100x + 200
    -198 = 100x
    -198/100 = x
    x = -99/50
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