Question

Solve each of the following equations and also verify your solution :

$\frac{x}{2}-\frac{4}{5}+\frac{x}{5}+\frac{3x}{10}=\frac{1}{5}$

Answer 1

$\frac{x}{2}-\frac{4}{5}+\frac{x}{5}+\frac{3x}{10}=\frac{1}{5}$
Adding $\frac{4}{5}$ to both sides,
$\frac{x}{2}+\frac{x}{5}+\frac{3x}{10}-\frac{4}{5}+\frac{4}{5}=\frac{1}{5}+\frac{4}{5}\Rightarrow \frac{x}{2}+\frac{x}{5}+\frac{3x}{10}=\frac{5}{5}=1\frac{5x+2x+3x}{10}=1$
(L.C.M. of~2,5,10 = 10)
$\frac{10x}{10}=1\Rightarrow x=1\therefore x=1$
Verification :
$L.H.S=\frac{x}{2}-\frac{4}{5}+\frac{x}{5}+\frac{3x}{10}=\frac{1}{2}-\frac{4}{5}+\frac{1}{5}+\frac{3}{10}=\frac{5-8+2+3}{10}=\frac{10-8}{10}=\frac{2}{10}=\frac{1}{5}=R.H.S.$