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Solve the fol...

Question

Solve the following inequality:
$\frac{0.5 x + 49}{10 x^{2} + x - 2} < \frac{1}{2}$

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Solution

$\frac{0.5 x + 49}{10 x^{2} + x - 2} < \frac{1}{2}$
$\frac{x + 98 - 10 x^{2} - x + 2}{2 (10 x^{2} + 5 x - 4 x - 2)} < 0$
$\frac{- 10 x^{2} + 100}{(5 x - 2) (2 x + 1)} < 0$
$\frac{x^{2} - 10}{(5 x - 2) (2 x + 1)} > 0$
$\frac{(x - 3.16) (x + 3.16)}{(5 x - 2) (2 x + 1)} > 0$
$x \in (- \infty, - 3.16) \cup (- 0.5, \frac{2}{5}) \cup (3.16, \infty)$

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