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Summation by Sigma Method

Solve the fol...

Question

Solve the following two- sided inequality:
$1 < \frac{3 x - 1}{2 x + 1} < 2$

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Solution

$1 < \frac{3 x - 1}{2 x + 1} < 2 ⟹ 1 < \frac{3}{2} - \frac{5}{2 (2 x + 1)} < 2$
$⟹ - \frac{1}{2} < - \frac{5}{2 (2 x + 1)} < \frac{1}{2} ⟹ \frac{- 1}{5} < \frac{1}{2 x + 1} < \frac{1}{5} ⟹ - 5 < 2 x + 1 < 5 ⟹ x \in (- 3, 2)$

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