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Homework Help: (23)/(120x) = 1/5. Solve for X

  1. Nov 25, 2013 #1


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    How is it done?

    Having to solve for X when X is in the denominator really confuses me. Please help!
  2. jcsd
  3. Nov 25, 2013 #2


    Staff: Mentor

    Just multiply both sides by 120*x and remember that this works as long as 120*x =/= 0 which means
    that x=/=0 in your final solution because dividing by zero is not defined.
  4. Nov 25, 2013 #3


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    Homework Helper

    Remember that

    [tex]a\cdot\frac{b}{c} = \frac{a}{c}\cdot b =\frac{ab}{c}[/tex]

    (The dot means multiply) so if we multiply


    by the denominator in the left fraction (which is 120x) then we get


    And now we can cancel 120x from the left side because

    [tex]120x\cdot\frac{23}{120x} = \frac{120x}{120x}\cdot 23 = 1\cdot 23=23[/tex]

    So we now have


    Now you can solve the rest in the usual way you've been solving equations.
    Also, keep in mind that you can have just multiplied through by x rather than 120x.
  5. Nov 25, 2013 #4


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    Education Advisor
    Gold Member

    This problem looks like it was made for cross multiplication, is that what they're teaching you right now?
  6. Nov 25, 2013 #5


    Staff: Mentor

    As an alternative, if two fractions are equal, then their reciprocals are equal.

    IOW, if a/b = c/d, then b/a = d/c, barring of course the possibility that any of the numbers are zero.

    In the context of this problem, you can rewrite 23/(120x) = 1/5 as 120x/23 = 5.
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