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Application of inequalities and absolute values

Solve the fol...

Question

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

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Solution

$\frac{x - 2}{x^{2} + 1} < \frac{- 1}{2}$
$2 x - 4 < - x^{2} - 1$
$x^{2} + 2 x - 3 < 0$
$(x + 3) (x - 1) < 0$
$x ϵ (- 3, 1)$

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Application of inequalities and absolute values

Standard XII Mathematics

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