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Thread: Linear Equations, Decimals

  1. #1
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    Linear Equations, Decimals

    Normally when I see a decimal in a linear equation I convert them to fractions and then find the LCD.

    For instance
    $\displaystyle .3(x-2)+.1+.4$
    $\displaystyle =\frac{3}{10}(x-2)+\frac{1}{10}=\frac{2}{5}$

    LCD of the above fractions = 10

    $\displaystyle =10[\frac{3}{10}(x-2)+\frac{1}{10}=\frac{2}{5}]$
    $\displaystyle =3(x-2)+1=4$
    $\displaystyle =3$

    However when trying to solve this particular linear equation with decimals the above manner does not seem to work.

    $\displaystyle .12-.4(x+1)+x=.5x+2$

    $\displaystyle =\frac{3}{25}-\frac{2}{5}(x+1)+x=\frac{1}{2}x+2$

    LCD of the above fractions = 50

    $\displaystyle =50[\frac{3}{25}-\frac{2}{5}(x+1)+x=\frac{1}{2}x+2]$

    Combine like terms
    $\displaystyle =-19x-14=25x+2$
    $\displaystyle =-12=44x$
    $\displaystyle x=\frac{-3}{11}$

    However this is the incorrect answer. The correct solution is 22.8. Is idea of converting the decimals to fractions incorrect, or did I go wrong somewhere else?

    Many Thanks
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  2. #2
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    Quote Originally Posted by allyourbass2212 View Post

    $\displaystyle .12-.4(x+1)+x=.5x+2$
    multiply every term by 100 to "clear" the decimals ...

    $\displaystyle 12 - 40(x+1) + 100x = 50x + 200
    $

    $\displaystyle 10x = 228$

    $\displaystyle x = 22.8$
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  3. #3
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    So I suppose converting them to fractions first simply doesnt work?
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  4. #4
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    Quote Originally Posted by allyourbass2212 View Post
    So I suppose converting them to fractions first simply doesnt work?

    It works ! Why not ..

    $\displaystyle 0.12-0.4(x+1)+x=0.5x+2$

    $\displaystyle \frac{12}{100}-\frac{4}{10}(x+1)+x=\frac{5}{10}x+2$

    Have it multiplied by 100
    $\displaystyle

    12-40(x+1)+100x=50x+200
    $

    which simplifies to $\displaystyle 10x=228$
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  5. #5
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    Ah I suppose it was because I was relying on my calculator to automatically convert the decimals to fractions.

    e.g instead of keeping .12 = 12/100 it will reduce it to 3/25 therefore throwing of my LCD etc

    Many thanks!
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