In the given problem, solve and graph. Express the answer in both inequality and interval notation. $2 x^{3} + x^{2} > 6 x$

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Solution

$2 x^{3} + x^{2} > 6 x$

$2 x^{3} + x^{2} - 6 x > 0$

$x (2 x^{2} + x - 6) > 0$

$x (x + 2) (2 x - 3) > 0$

$- 2 < x < 0 o r x > \frac{3}{2}$

$⎡ ⎢ ⎢ ⎢ ⎣ \begin{matrix} S o l u t i o n : & - 2 < x < 0 o r x > \frac{3}{2} D e c i m a l : & - 2 < x < 0 o r x > 1.5 I n t e r v a l N o t a t i o n : & (- 2, 0) \cup (\frac{3}{2}, \infty) \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎦$

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