Solve the linear equation 3t - 2 4 - 2t + 3 3 = 2 3 - t. - Vidyadip

Question

Solve the linear equation $\frac{{3t - 2}}{4} - \frac{{2t + 3}}{3} = \frac{2}{3} - t$.

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Answer

$\frac{{3t - 2}}{4} - \frac{{2t + 3}}{3} = \frac{2}{3} - t$ It is a linear equation since it involves linear expressions only.
$\therefore \frac{3}{4}t - \frac{2}{4} - \frac{2}{3}t - \frac{3}{3} = \frac{2}{3} - t$
$\therefore \frac{3}{4}t - \frac{1}{2} - \frac{2}{3}t - 1 = \frac{2}{3} - t$
$\therefore \frac{3}{4}t - \frac{2}{3}t + t = \frac{2}{3} + \frac{1}{2} + 1$ ... [Transposing –t to $L.H.S.$ and $ - \frac{1}{2}$ and –1 to $R.H.S.]$
$\therefore \frac{{9t - 8t + 12t}}{{12}} = \frac{{4 + 3 + 6}}{6}$
$\therefore \frac{{13t}}{{12}} = \frac{{13}}{6}$
$\therefore t = \frac{{13}}{6} \times \frac{{12}}{{13}}$ ... [Multiplying both sides by $\frac{{12}}{{13}}$]
$\therefore t = 2$ this is the required solution.

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