Is the equalities true or not and please please explain why

Is the equalities true or not? and please please explain why or why not?

x^3 - x=O(x^4)

discrete mathematics

Solution

True

x^3-x<x^4+x^4

for all x>1

ie

x^3-x<2x^4

But a better estimate is:

x^3-x<x^3+x^3=2x^3, for all x>1

x^3-x=O(x^3)