Question
Solve $\frac{x}{2}+\frac{x}{4}+\frac{x}{5}+10000=x$.
✓
Answer
We have, $\frac{x}{2}+\frac{x}{4}+\frac{x}{5}+10000=x$
$\Rightarrow \quad \frac{x}{2}+\frac{x}{4}+\frac{x}{5}-x=-10000\quad$ [transposing $x$ to LHS and 10000 to RHS]
$\Rightarrow \quad \frac{10 x+5 x+4 x-20 x}{20}=-10000$
$\Rightarrow \quad \frac{19 x-20 x}{20}=-10000$
$\Rightarrow \quad \frac{-x}{20}=-10000$
$\therefore \quad x=200000$
$\Rightarrow \quad \frac{x}{2}+\frac{x}{4}+\frac{x}{5}-x=-10000\quad$ [transposing $x$ to LHS and 10000 to RHS]
$\Rightarrow \quad \frac{10 x+5 x+4 x-20 x}{20}=-10000$
$\Rightarrow \quad \frac{19 x-20 x}{20}=-10000$
$\Rightarrow \quad \frac{-x}{20}=-10000$
$\therefore \quad x=200000$
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