Answer: -10<x<0 or x>1
Explanation:
Let's solve your inequality step-by-step.
x^3+9x^2-10x>0
Let's find the critical points of the inequality.
x^3+9x^2-10x=0
x(x-1)(x+10)=0 (Factor left side of equation)
x=0 or x-1=0 or x+10=0 (Set factors equal to 0)
x=0 or x=1 or x= -10
Check intervals in between critical points. (Test values in the intervals to see if they work.)
x<-10 (Doesn't work in original inequality)
-10<x<0 (Works in original inequality)
x<0<1 (Doesn't work in original inequality)
x>1 (Works in original inequality)
Answer: -10 < x < 0 OR x > 1