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Definition of Functions

Solve the fol...

Question

Solve the following inequality:
$| x - 6 | > x^{2} - 5 x + 9$

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Solution

$| x - 6 | > x^{2} - 5 x + 9$

$x - 6 \geq 0 : x \geq 6, | x - 6 | = x - 6$

$x - 6 < 0 : x < 6, | x - 6 | = - (x - 6)$

$x^{2} - 5 x + 9 < - (x - 6)$

$x^{2} - 5 x + 9 - (- (x - 6)) < 0$

$x^{2} - 4 x + 3 < 0$

$(x - 3) (x - 1) < 0$

$1 < x < 3$

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