Solve each of the following equations and also verify your solution :

$\frac{3 x}{4} - \frac{(x - 1)}{2} = \frac{(x - 2)}{3}$

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Solution

$\frac{3 x}{4} - \frac{(x - 1)}{2} = \frac{(x - 2)}{3} = \frac{9 x - 6 (x - 1) = 4 (x - 2)}{12}$
(L.C.M. of 4, 2, 3 = 12)
$\Rightarrow 9 x - 6 x + 6 = 4 x - 8$
$\Rightarrow 9 x - 6 x - 4 x = - 8 - 6$ (By transposition)
$\Rightarrow 9 x - 10 x = - 14 \Rightarrow - x = - 14 ∴ x = 14$
Verification:
$L . H . S . = \frac{3 x}{4} - \frac{x - 1}{2} = \frac{3 \times 14}{4} - \frac{14 - 1}{2} = \frac{21}{2} - \frac{13}{2} = \frac{21 - 13}{2} = \frac{8}{2} = 4 R . H . S . = \frac{x - 2}{3} = \frac{14 - 2}{3} = \frac{12}{3} = 4 ∴ L . H . S . = R . H . S .$

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