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Functions

Solve 2x+3 ...

Question

Solve $\frac{2 x + 3}{x^{2} + x - 12} < \frac{1}{2}$

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Solution

$\frac{2 x + 3}{x^{2} + x - 12} - \frac{1}{2} < 0$

=> $\frac{- x^{2} + 3 x + 18}{x^{2} + x - 12} < 0$

Multiply by -1 on both side,

=> $\frac{x^{2} - 3 x - 18}{x^{2} + x - 12} > 0$

=> $\frac{(x + 3) (x - 6)}{(x + 4) (x - 3)} > 0$

Therefore,

=> $x ϵ (- 4, - 3) \cup (0, 3) \cup (6, \infty)$

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