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

$\frac{a - 8}{3} = \frac{a - 3}{2}$

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Solution

$\frac{a - 8}{3} = \frac{a - 3}{2}$
By cross multiplication:
$2 (a - 8) = 3 (a - 3) 2 a - 16 = 3 a - 9$
$\Rightarrow 2 a - 3 a = - 9 + 16$ (By transposition)
$\Rightarrow - a = 7 \Rightarrow a = - 7 ∴ a = - 7$
Verification:
$L . H . S = \frac{a - 8}{3} = \frac{- 7 - 8}{3} = \frac{- 15}{3} = - 5 R . H . S = \frac{a - 3}{2} = \frac{- 7 - 3}{2} = \frac{- 10}{2} = - 5 ∴ L . H . S . = R . H . S .$

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