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

$\frac{5 x}{3} - \frac{(x - 1)}{4} = \frac{(x - 3)}{5}$

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Solution

$\frac{5 x}{3} - \frac{(x - 1)}{4} = \frac{(x - 3)}{5} = \frac{100 x - 15 (x - 1) = 12 (x - 3)}{60}$
(L.C.M. of 3, 4, 5 = 60)
$100 x - 15 x + 15 = 12 x - 36 100 x - 15 x - 12 x = - 36 - 15$
(By transposition)
$\Rightarrow 100 x - 27 x = - 51 \Rightarrow 73 x = - \frac{51}{3} \Rightarrow x = \frac{- 51}{73} ∴ x = \frac{- 51}{73}$
Verification :
$L . H . S = \frac{5 x}{3} - \frac{x - 1}{4} = \frac{5 \times (- 51)}{3 \times 73} - \frac{\frac{- 51}{73} - 1}{4} = \frac{- 85}{73} - \frac{- 51 - 73}{4 \times 73} = \frac{- 85}{73} + \frac{124}{4 \times 73} = \frac{- 85}{73} + \frac{31}{73} = \frac{- 85 + 31}{73} = \frac{- 54}{73} R . H . S . = \frac{x - 3}{5} = \frac{\frac{- 51}{73} - 3}{5} = \frac{- 51 - 219}{73 \times 5} = \frac{- 270}{73 \times 5} = \frac{- 54}{73} ∴ L . H . S . = R . H . S .$

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