Question

Solve the linear equation $\frac{x}{2}-\frac{1}{5}=\frac{x}{3}+\frac{1}{4}$

Answer 1

$\frac{x}{2}-\frac{1}{5}=\frac{x}{3}+\frac{1}{4}$
L.C.M. of the denominators, $2, 3, 4$, and $5$, is $60$.
Multiplying both sides by $60$, we obtain

$60\bigg(\frac{x}{2}-\frac{1}{5}\bigg)=60\bigg(\frac{x}{3}+\frac{1}{4}\bigg)$

$\Rightarrow$ $30x - 12$ = $20x + 15$ (Opening the brackets)
$\Rightarrow$ $30x - 20x$ = $15 + 12$
$\Rightarrow$ $10x = 27$
$\Rightarrow$ $x = \frac{27}{10}$