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Math Help - Fractional Equation

  1. #1
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    Question Fractional Equation

    (x-2)/2 - (x-8)/4 = 1/2

    I think I am supposed to solve this as a proportion... but not sure
    I would show my work, but I have tried this so many times it's not funny... I have gotten x=2, x=4, x=6, x=14, x=16... you get it... LOL
    any help is greatly appreciated!!!
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  2. #2
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    Re: Fractional Equation

    Multiply everything by 4.

     \frac{4(x-2)}{2} -  \frac{4(x-8)}{4}= \frac{4\times1}{2}
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  3. #3
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    Re: Fractional Equation

    I ran out the equation like that and got x=4...
    (x-2)/2 - (x-8)/4 = 1/2
    (4x-8)/2 - (4x-8)/4 = 4/2
    (2x-4) - (x-2) = 2
    x-2 = 2
    x = 4

    I know I have to be doing something wrong, just not sure what it is... (btw, how do you get the fractions like that???)
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  4. #4
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    Re: Fractional Equation

    understand that the whole reason for multiplying each term by 4 is to clear the fractions ...

    \frac{4(x-2)}{2} - \frac{4(x-8)}{4} = \frac{4}{2}

    2(x-2) - (x-8) = 2

    now finish it ...
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  5. #5
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    Re: Fractional Equation

    Quote Originally Posted by Drummerman View Post
    (x-2)/2 - (x-8)/4 = 1/2

    I think I am supposed to solve this as a proportion... but not sure
    I would show my work, but I have tried this so many times it's not funny... I have gotten x=2, x=4, x=6, x=14, x=16... you get it... LOL
    any help is greatly appreciated!!!
    An alternative (better) method is to try to simplify the LHS before trying to solve anything. To do this, you would need to add the fractions, and to add fractions you need a common denominator. In this case, the lowest common denominator is 4.

    \displaystyle \begin{align*} \frac{x - 2}{2} - \frac{x - 8}{4} &= \frac{1}{2} \\ \frac{x - 2}{2} \cdot \frac{2}{2} - \frac{x - 8}{4} &= \frac{1}{2} \\ \frac{2x - 4}{4} - \frac{x - 8}{4} &= \frac{1}{2} \\ \frac{2x - 4 - (x - 8)}{4} &= \frac{1}{2} \\ \frac{x + 4}{4} &=\frac{1}{2}  \end{align*}

    This explains why multiplying by 4 is appropriate, it's because the simplification of the LHS gives 4 as the denominator, which then needs to be multiplied out.
    Thanks from Drummerman
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  6. #6
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    Re: Fractional Equation

    Yes, that is an alternative method- but I don't understand why you say it is better.
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  7. #7
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    Re: Fractional Equation

    Quote Originally Posted by HallsofIvy View Post
    Yes, that is an alternative method- but I don't understand why you say it is better.
    It is considered more elegant mathematically to simplify all equations before trying to solve them, as it makes the process of solving the equation much easier.
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  8. #8
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    Thumbs up Re: Fractional Equation

    thanks ProveIt!!! that helped so much!!!
    I did this:
    \displaystyle \begin{align*} 4*\frac{x+4}{4}&=4*\frac{1}{2}\\x+4&=2\\x&=(-2) \end{align*}
    Thanks again for the help!!!
    Last edited by Drummerman; April 24th 2012 at 09:35 AM.
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