Question

Solve the linear equation: $\frac{x-5}{3}=\frac{x-3}{5}$

Answer 1

$\frac{x-5}{3}=\frac{x-3}{5}$
L.C.M. of the denominators, $3$ and $5$, is $15$.
Multiplying both sides by $15$, we obtain
$5(x - 5) = 3(x - 3)$
$\Rightarrow$ $5x - 25 = 3x - 9$ (Opening the brackets)
$\Rightarrow$ $5x - 3x = 25 - 9$
$\Rightarrow$ $2x = 16$
$\Rightarrow$ $x$ = $\frac{16}{2}$
$\Rightarrow$ $x = 8$