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

$\frac{7 y + 2}{5} = \frac{6 y - 5}{11}$

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Solution

$\frac{7 y + 2}{5} = \frac{6 y - 5}{11}$
By cross multiplication,
$11 (7 y + 2) = 5 (6 y - 5)$
$\Rightarrow 77 y + 22 = 30 y - 25$
$\Rightarrow 77 y - 30 y = - 25 - 22$ (By transposition)
$\Rightarrow 47 y = - 47$
$\Rightarrow y = \frac{- 47}{47} = - 1 ∴ y = - 1 L . H . S . = \frac{7 y + 2}{5} = \frac{7 \times (- 1) + 2}{5} = \frac{- 7 + 2}{5} = \frac{- 5}{5} = - 1 R . H . S . = \frac{6 y - 5}{11} = \frac{6 (- 1) - 5}{11} = \frac{- 6 - 5}{11} = \frac{- 11}{11} = - 1 ∴ L . H . S . = R . H . S .$

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