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How do I solve an equation with a fraction as the variable's coefficient?

  1. Sep 7, 2011 #1
    It's been two years since Algebra I, and I forgot a lot. I'm doing a review of solving equations, and every single one includes fractions. I don't like fractions.

    The easiest one is as follows (simplified to an improper fraction): 4/3x = 5.

    If I remember anything about solving equations with fractions as coefficients, the phrase "Multiply by the reciprocal" comes to mind. I vaguely remember doing this by flipping the fraction and multiplying, but I don't remember what I multiply by.

    I can't find anything on the internet about this, so I'm hoping someone can explain how to do this. Help is greatly appreciated!

    Last edited: Sep 7, 2011
  2. jcsd
  3. Sep 7, 2011 #2


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    Staff: Mentor

    I moved your thread for you. Thanks for the heads-up.

    In general, you want to do the same operation to both sides of the = sign, so that the equality still holds true.

    So you can add the same thing to both the LHS (lefthand side) and RHS, or multiply LHS and RHS by the same thing, etc.

    So if you want to get the "x" out of the denominiator of the LHS, what can you multiply both the LHS and RHS by to get the x out of the denominator of the LHS and into the numerator of the RHS?

    Remember that if you have the same thing in both the numerator and denominator, you can "cancel" them because x/x = 1, for any x (ignore x=0 for now).
  4. Sep 7, 2011 #3


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    Homework Helper

    So we're looking at (4/3)x = 5. Remember to use parentheses.

    Yes...what's the reciprocal of 4/3? Multiply both sides by this and you have your answer.


    If you do mean 4/(3x) = 5, then follow berkeman's advice.
  5. Sep 7, 2011 #4


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    Staff: Mentor

    Oh. Is it (4/3)x=5, or (4/3x)=5 ?
  6. Sep 7, 2011 #5
    Thank you all! It was meant to be (4/3)x = 5. Wasn't sure how to describe a fraction there.
  7. Sep 7, 2011 #6


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    Staff: Mentor

    You can also use LaTeX to help you write your equations. Use the Quote button on my post to see how I did this:

    [tex]\frac{4}{3} x = 5[/tex]

    In the Edit (Advanced) window, the LaTeX tools are under the Sigma button, which looks like this:

  8. Sep 7, 2011 #7
    Good to know, thanks.
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