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Math Help - Basic algebra question, confused

  1. #1
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    Basic algebra question, confused

    I didnt know how to name this topic, but hopefully someone can help

    heres the equation:
    (one-fourth y minus two thirds y equals 5)
    1/4y - 2/3y = 5

    I have the answer, which is -12. But can someone explain to me HOW to get the answer without plugging -12 in? When I start moving numbers to the other side I end up getting a number thats waay off by the end of it.

    Thank you!
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  2. #2
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    Multiply every term by 12.
    Then solve the equation you get.
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  3. #3
    Senior Member yeKciM's Avatar
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    Quote Originally Posted by NecroWinter View Post
    I didnt know how to name this topic, but hopefully someone can help

    heres the equation:
    (one-fourth y minus two thirds y equals 5)
    1/4y - 2/3y = 5

    I have the answer, which is -12. But can someone explain to me HOW to get the answer without plugging -12 in? When I start moving numbers to the other side I end up getting a number thats waay off by the end of it.

    Thank you!
     \displaystyle \frac {y}{4} -\frac {2y}{3} = 5

    multiply all by 12

     3y-8y=60 \Rightarrow 5y=-60 \Rightarrow y = -12

    or is it

     \displaystyle \frac {1}{4y} - \frac {2}{3y} = 5



    Edit : Sorry Plato, didn't see that you have posted answer ...
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  4. #4
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    Quote Originally Posted by NecroWinter View Post
    I didnt know how to name this topic, but hopefully someone can help

    heres the equation:
    (one-fourth y minus two thirds y equals 5)
    1/4y - 2/3y = 5

    I have the answer, which is -12. But can someone explain to me HOW to get the answer without plugging -12 in? When I start moving numbers to the other side I end up getting a number thats waay off by the end of it.

    Thank you!
    Two-thirds of some number subtracted from a quarter of the same number equals 5.

    \displaystyle\ y\left(\frac{1}{4}\right)-y\left(\frac{2}{3}\right)=5\Rightarrow\ y\left(\frac{1}{4}-\frac{2}{3}\right)=5

    A quarter is just a value where the denominator is 4 times the numerator.

    \displaystyle\frac{1}{4}=\frac{2}{8}=\frac{3}{12}=  \frac{4}{16}=.....

    Also

    \displaystyle\frac{2}{3}=\frac{2}{2}\cdot\frac{2}{  3}=\frac{4}{6}=\frac{8}{12}=....

    We can add and subtract fractions with the same denominator...

    \displaystyle\ y\left(\frac{3}{12}-\frac{8}{12}\right)=y\left(-\frac{5}{12}\right)

    \displaystyle\ -\frac{5}{12}\left(-\frac{12}{5}\right)=1

    Therefore...

    \displaystyle\ y=\left(-\frac{12}{5}\right)5

    Since LHS=RHS, then 12(LHS)=12(RHS)

    so a shortcut is to multiply both sides by 12 to avoid having to combine the fractions.
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