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

  1. Nov 25, 2013 #1

    939

    User Avatar

    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

    jedishrfu

    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

    Mentallic

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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

    [tex]\frac{23}{120x}=\frac{1}{5}[/tex]

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

    [tex]120x\cdot\frac{23}{120x}=120x\cdot\frac{1}{5}[/tex]

    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

    [tex]23=\frac{120x}{5}[/tex]

    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

    Student100

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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

    Mark44

    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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