Question

solve the eniquality.

x^3-x greater than or equal to 0

Answer 1

this is the first step:

x^3 - x = x(x^2 - 1) = x(x + 1)(x - 1)

Answer 2

x(x+1)(x-1) >= 0

Answer 3

eigenschmeigen you can also help me in a min too mate

Answer 4

now we have this product. first consider the roots:

x = -1, x = 0 , x= 1

now consider the cases

x=<-1 , -1=<x=<0 , 0=<x=<1 , 1=<x

Answer 5

oh ok so once you distribute you just set it equal to zero and find them?

Answer 6

yes.

in fact, most of this is unnecessary, but its good practice for harder problems

drawing a graph helps: