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Math Help - 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
    .3(x-2)+.1+.4
    =\frac{3}{10}(x-2)+\frac{1}{10}=\frac{2}{5}

    LCD of the above fractions = 10

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

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

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

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

    LCD of the above fractions = 50

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

    Combine like terms
    =-19x-14=25x+2
    =-12=44x
    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

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

    12 - 40(x+1) + 100x = 50x + 200<br />

    10x = 228

    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 ..

    0.12-0.4(x+1)+x=0.5x+2

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

    Have it multiplied by 100
     <br /> <br />
12-40(x+1)+100x=50x+200<br />

    which simplifies to 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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