Answer
$(-∞, -1) U (1, 7)$
Work Step by Step
$x (1-x^2)^3 < 7 (1-x^2)^3$
Find the roots of the function
$x (1-x^2)^3 - 7 (1-x^2)^3 < 0$
$((1+x)(1-x))^3 (x-7) $
$x = -1 ,1, 7$
Test numbers in between those zero values to determine if the function is negative or positive
(-∞, -1) $(-)(-)(-) = (-)$
(-1, 1) $(+)(-)(-) = (+)$
(1, 7) $(+)(+)(-) = (-)$
(7, ∞) $(+)(+)(+) = (+)$
Thus the solution is $(-∞, -1) U (1, 7)$
