Answer:
(x < 0) ∪ (x > 1/2)
Explanation:
First inequality:
x^3 < 0
x < 0 . . . . . take the cube root
Second inequality:
4x^4 > x^2
4x^4 -x^2 > 0
x^2(4x^2 -1) > 0
Any non-zero x will make the first factor positive. The product will be positive only when the second factor is positive, for x^2 > 1/4
x^2 > 1/4
|x| > 1/2 . . . . . take the square root
x < -1/2 or x > 1/2
The first part of this solution is already covered by the solution to the first inequality. Hence the solution set for the system of inequalities is ...
(x < 0) ∪ (x > 1/2)