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

$x - 2 x + 2 - \frac{16}{3} x + 5 = 3 - \frac{7}{2} x$

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Solution

$x - 2 x + 2 - \frac{16}{3} x + 5 = 3 - \frac{7}{2} x$
$\Rightarrow x - 2 x - \frac{16}{3} x + \frac{7}{2} x = 3 - 2 - 5$ (By transposition)
$\Rightarrow \frac{6 x - 12 x - 32 x + 21 x}{6} = - 4 \frac{27 x - 44 x}{6} = - 4 \Rightarrow - 17 x = - 4 \times 6 = - 24 \Rightarrow x = \frac{- 24}{- 17} = \frac{24}{17} ∴ x = \frac{24}{17}$
Verification:
$L . H . S . = x - 2 x + 2 - \frac{16}{3} x + 5 = - x - \frac{16}{3} x + 7 = \frac{- 24}{17} - \frac{16}{3} \times \frac{24}{17} + 7 = \frac{- 24}{17} - \frac{128}{17} + 7 = \frac{- 152}{17} + 7 = \frac{- 152 + 119}{17} = \frac{- 33}{17} R . H . S . = 3 - \frac{7}{2} x = 3 - \frac{7}{2} \times \frac{24}{17} = 3 - \frac{84}{17} = \frac{51 - 84}{17} = \frac{- 33}{17} ∴ L . H . S . = R . H . S .$

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