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Math Help - Variable, reciprocals, and fractions..

  1. #1
    Newbie Cyberman's Avatar
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    Variable, reciprocals, and fractions..

    I came across another question which has just stumped me because I worked it over about 5 times and I couldn't figure out how the book got the answer. I've obtained messed up answers and none have them have been...

    Answer: 6

    Problem:

    2x - 3(x-2)/2 = 7 - x-3/3

    The thing that probably messed me up the most was the fact that I didn't know how to get the variable fractions out of the way.

    I really don't remember the book covering that, therefore I sucked at it.

    I did somehow try to solve it:

    2(2x - 3(x-2)/2) = (7 - x-3/3)2
    4x - 3x - 6 = 14 - 2x-6/3

    x - 6 = 14... +6+14...

    x = 20 - 2x-6/6
    3(x) = (20 - 2x-6/3)3
    3x = 60 - 2x - 6
    +2x
    8x = 54
    8/8 = 54/8
    = 6.75


    So basically i'm screwing up somewhere and I don't know where but I'm not getting the right answer.
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  2. #2
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    2 times -3 times (x-2)/2 is -3x + 6 not -3x -6
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  3. #3
    MHF Contributor
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    Here is one way

    My favorite way in dealing with fractions in equations is to eliminate the fractions first. Make all numbers as whole numbers.

    In doing that, I multiply both sides of the equations by a common multiplier. This common multiplier is the product of all the denominators, but no denominator is to repeat or appear more than once.

    2x - 3(x-2)/2 = 7 - x-3/3

    Rewriting that,
    2x - 3(x-2)/2 = 7 -(x-3)/3

    There are two fractions, so two denominators: 2 and 3.
    Clear the fractions, multiply both sides by 2*3,
    2*3*2x -3*3(x-2) = 2*3*7 -2*(x-3)
    12x -9(x-2) = 42 -2(x-3)
    12x -9x +18 = 42 -2x +6
    Collect like terms, or isolate the x,
    12x -9x +2x = 42 +6 -18
    5x = 30
    x = 30/5 = 6 ----answer.
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  4. #4
    Newbie Cyberman's Avatar
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    Quote Originally Posted by rgep
    2 times -3 times (x-2)/2 is -3x + 6 not -3x -6
    Righto, thanks.
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