Answer
$(-∞, -3) U (1/2, 3)$
Work Step by Step
$2x^3 - 18x < x^2 - 9$
Find the roots of the function
$2x^3 - x^2 - 18x + 9$
$x^2(2x - 1) - 9 (2x -1)$
$(x^2 - 9) (2x-1)$
$(x+3)(2x-1)(x-3)$
$x = -3, 1/2, 3$
Test numbers in between those zero values to determine if the function is negative or positive
(-∞, -3) $(-)(-)(-) = (-)$
(-3, 1/2) $(+)(-)(-) = (+)$
(1/2, 3) $(+)(+)(-) = (-)$
(3, ∞) $(+)(+)(+) = (+)$
Thus the solution is $(-∞, -3) U (1/2, 3)$
