Question 771758
You said the magic word, so I'm your man!
Given:
(1) x^3 - 4x >= 0
This factors into 3 factors
(2) x*(x^2 - 4) >= 0 or
(3) x*(x - 2)*(x + 2) >= 0
The product of three terms is positive (greater or equal to zero) if all three of the them are positive or one is positive and the other two are negative.
Applying this condition to (3) we get
(4) all positive when x >= +2 and
(5) the first two are negative when -2 < x < 0
Answer: The inequality holds in two sections of the real line, when -2 < x < 0 and x > +2. You can graph this answer, but I can't do it here. The "empty" sections are x <= -2 and 0 <= x < +2).