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Math Help - Question regarding frations with variables?

  1. #1
    Newbie fetuslasvegas's Avatar
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    Question regarding frations with variables?

    Hello, I feel ridiculous asking this question but I just cannot remember.

    This is my problem:

    5/6x+1/2=5/3x

    I know I am supposed to get the common denominator, but how do I do that when the X variable is on one denominator and not the other?

    Thank you!!
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  2. #2
    Pim
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    I feel that, rather than getting the common denominatior and cross-multiplying, this question is better solved by moving the x's to the RHS

    5/6x + 1/2 = 5/3x
    1/2 = 5/3x-5/6x
    1/2 = 10/6x-5/6x
    1/2 = 5/6x
    x = 6/10 = 3/5
    Last edited by Pim; May 24th 2010 at 11:44 AM. Reason: Mistake
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  3. #3
    Newbie fetuslasvegas's Avatar
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    My teacher gave us the answer of x=5/3, is that wrong?
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  4. #4
    Junior Member allsmiles's Avatar
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    ok, i think i have this, but not 100% sure.

    step one: because it is a fraction, you owuld mult. both sides by 6x = 1.
    then you would be left of with 5/1 + 1/2. which i hope you can do.

    the other side is where i get confuesd. you have to cross mult, and if you did this, you would end up witha fraction again. is that what you are supost to get??
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  5. #5
    Pim
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    Quote Originally Posted by fetuslasvegas View Post
    my teacher gave us the answer of x=5/3, is that wrong?
    5/6*5/3 + 1/2 = 1 8/9
    5/3*5/3 = 25/9 = 2 7/9
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  6. #6
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    e^(i*pi)'s Avatar
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    Quote Originally Posted by fetuslasvegas View Post
    Hello, I feel ridiculous asking this question but I just cannot remember.

    This is my problem:

    5/6x+1/2=5/3x

    I know I am supposed to get the common denominator, but how do I do that when the X variable is on one denominator and not the other?

    Thank you!!
    It could be due to the ambiguity. Do you mean 5/6x or 5x/6 for example?

    I am assuming you mean \frac{5}{6x} + \frac{1}{2} = \frac{5}{3x}

    Multiply through by 6x

    5 + 3x = 10

    Solve for x = \frac{5}{3}
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  7. #7
    Newbie fetuslasvegas's Avatar
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    I'm still really confused, would you mind putting in words because I'm not understanding what's going on with just numbers
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  8. #8
    MHF Contributor harish21's Avatar
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    Quote Originally Posted by fetuslasvegas View Post
    I'm still really confused, would you mind putting in words because I'm not understanding what's going on with just numbers

    \frac{5}{6x} + \frac{1}{2} = \frac{5}{3x}

    \frac{5}{6x} -  \frac{5}{3x} = - \frac{1}{2}

    \frac{5}{6x} - \frac{10}{6x} = \frac{-1}{2}

    \frac{5-10}{6x} = \frac{-1}{2}

    \frac{-5}{6x} = \frac{-1}{2}

    cross multiplication gives:

    6x = 10

    x = \frac{5}{3}

    Clear??
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  9. #9
    Newbie fetuslasvegas's Avatar
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    Quote Originally Posted by e^(i*pi) View Post
    It could be due to the ambiguity. Do you mean 5/6x or 5x/6 for example?

    I am assuming you mean \frac{5}{6x} + \frac{1}{2} = \frac{5}{3x}

    Multiply through by 6x

    5 + 3x = 10

    Solve for x = \frac{5}{3}

    Yes that is what I meant, sorry I wasn't sure how to actually make fractions on here.

    Ok I'm understanding a little better, the only thing I'm confused about it the 5+3x=10?? How do you get 10?


    Sorry I'm terrible at fractions and math in general.
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  10. #10
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    e^(i*pi)'s Avatar
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    Quote Originally Posted by fetuslasvegas View Post
    I'm still really confused, would you mind putting in words because I'm not understanding what's going on with just numbers
    You are given: \frac{5}{6x} + \frac{1}{2} = \frac{5}{3x}

    Multiply each term by 6x as this is the lowest common denominator of 2, 3 \text{ and } 6x (Just like 24 is the lowest common denominator of 3,4 and 6)

    Multiplying by the LCD will remove the fraction to give a simple linear equation

    \frac{5}{6x} \cdot 6x + \frac{1}{2} \cdot 6x = \frac{5}{3x} \cdot 6x

    When you do some cancelling you get 5+3x=10. Can you find x from this last equation?
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  11. #11
    Newbie fetuslasvegas's Avatar
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    Quote Originally Posted by e^(i*pi) View Post
    You are given: \frac{5}{6x} + \frac{1}{2} = \frac{5}{3x}

    Multiply each term by 6x as this is the lowest common denominator of 2, 3 \text{ and } 6x (Just like 24 is the lowest common denominator of 3,4 and 6)

    Multiplying by the LCD will remove the fraction to give a simple linear equation

    \frac{5}{6x} \cdot 6x + \frac{1}{2} \cdot 6x = \frac{5}{3x} \cdot 6x

    When you do some cancelling you get 5+3x=10. Can you find x from this last equation?


    OHHH OHHH I get it!! Thank you!!!
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