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