Question

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

Answer 1

$x-\frac{1}{5}=\frac{x}{3}+\frac{1}{4}$
Transpose $\frac{x}{3}$ to LHS and $\frac{1}{5}$ to RHS

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

LHS $\Rightarrow x-\frac{x}{3}\Rightarrow LCM\Rightarrow 3$

$\frac{3x-1x}{3}=\frac{2x}{3}$ ....(i)

RHS $\Rightarrow \frac{1}{4}+\frac{1}{5},LCM=20$

$\Rightarrow \frac{5+4}{20}=\frac{9}{20}$ ..... (2)

Equate $\left(1\right)$ and $\left(2\right)$

$\frac{2x}{3}=\frac{9}{20}$

Multiply both sides by $60$
We will get
$\frac{2x}{3}\times 60=\frac{9}{20}\times 60$

$2x\times 20=9\times 3$

$40x=27$

$x=\frac{27}{40}$