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Integration of Irrational Algebraic Fractions - 2

Solve the fol...

Question

Solve the following inequality:
$3 x^{2} - | x - 3 | > 9 x - 2.$

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Solution

$3 x^{2} - | x - 3 | > 9 x - 2$

$3 x^{2} - x + 3 > 9 x - 2, 3 x^{2} + x - 3 > 9 x - 2$

$3 x^{2} - x + 3 - 9 x + 2 > 0, 3 x^{2} + x - 3 - 9 x + 2 > 0$

$3 x^{2} - 10 x + 5 > 0, 3 x^{2} - 8 x - 1 > 0$

$x < \frac{4 - \sqrt{19}}{3}, x > \frac{4 + \sqrt{19}}{3}$

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