1. ## 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

2. Originally Posted by allyourbass2212

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

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

$\displaystyle 10x = 228$

$\displaystyle x = 22.8$

3. So I suppose converting them to fractions first simply doesnt work?

4. Originally Posted by allyourbass2212
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 $\displaystyle 10x=228$

5. 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!