Find the largest integral $x$ which satisfies the following inequality:
$\frac{x - 2}{x^{2} - 9} < 0$

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Solution

$\frac{x - 2}{x^{2} - 9} < 0$
$\frac{x - 2}{(x - 3) (x + 3)} < 0$
$x ϵ (- \infty, - 3) \cup (2, 3)$
largest $x = - 4$

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