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Concept of Inequality

Solve the fol...

Question

Solve the following inequality:
$| x^{2} + 4 x | - 5 < 0.$

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Solution

$| x^{2} + 4 x | - 5 < 0$
$| x^{2} + 4 x | < 5$
$x^{2} + 4 x > - 5$
$x^{2} + 4 x + 5 > 0$
$b < 0$
$x ϵ R$
$x^{2} + 4 x < 5$
$x^{2} + 4 x - 5 < 0$
$x^{2} + 5 x - x - 5 < 0$
$(x - 1) (x + 5) < 0$
$x ϵ (- 5, 1)$
So, $x ϵ (- 5, 1)$

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