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Thread: Solving fractions for X

  1. #1
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    Solving fractions for X

    Starting to learn latex and also need to some help: I am trying to solve the equation below:

    $\displaystyle \frac{x}{7} - \frac{1}{2} = 1 - \frac{2x}{5}$

    The only thing I can think to do is start multiplying out the $\displaystyle \frac{1}{2}$:


    $\displaystyle 2\frac{x}{7} - = 2 x 1 - 2\frac{2x}{5}$

    or to find a common denominator on the left:

    $\displaystyle \frac{2x -7}{14} = 1 - \frac{2x}{5}$

    Either way after these I am getting lost if anyone could point out the right direction to me would be great.

    Thanks
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  2. #2
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    The first step is to perform the subtractions on each side by getting a common denominator.
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  3. #3
    Super Member TheChaz's Avatar
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    $\displaystyle \frac{x}{7} - \frac{1}{2} = 1 - \frac{2x}{5}$
    You could multiply everything by the LCD (which will be 7*2*5 = 70).
    Then you'll have 10x - 35 = 70 - 28x.
    Can you take it from here?
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  4. #4
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    Ok so tell me if I got this right:

    $\displaystyle 10x - 35 = 70 - 28x$

    Then I

    $\displaystyle 10x + 28x - 35 = 70 $

    $\displaystyle 38x - 35 = 70 $

    $\displaystyle 38x = 70 + 35 $

    $\displaystyle x = \frac {70 + 35}{38} $

    $\displaystyle x = 2\frac {29}{38} $

    Sorry for all the question hopefully im close to the answer now
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  5. #5
    Super Member TheChaz's Avatar
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    I'd just leave it as x = 105/38, but that's just me...
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