Solve the linear equation x - 5 3 = x - 3 5 . - Vidyadip

Question

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

✓

Answer

$\frac{{x - 5}}{3} = \frac{{x - 3}}{5}$
It is a linear equation since it involves linear expressions only.
$\therefore$ $\frac{x}{3} - \frac{5}{3} = \frac{x}{5} - \frac{3}{5}$
$\therefore$ $\frac{x}{3} - \frac{x}{5} = \frac{3}{5} + \frac{5}{3}$ ... [Transposing $\frac{x}{5}$ to $L.H.S$. and $\frac{{ - 5}}{3}$ to $R.H.S.]$
$\therefore \frac{{5x - 3x}}{{15}} = \frac{{25 - 9}}{{15}}$
$\therefore \frac{{2x}}{5} = \frac{{16}}{{15}}$
$\therefore x = \frac{{16}}{{15}} \times \frac{{15}}{2}$ ... [Multiplying both sides by $\frac{{15}}{2}$]
$\therefore x = 8$
this is the required solution.
Verification,
L.H.S. = $\frac{{8 - 5}}{3} = \frac{3}{3} = 1$
R.H.S. = $\frac{{8 - 3}}{5} = \frac{5}{5} = 1$
Therefore, $L.H.S. = R.H.S.$

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