Solve the non-linear inequality:

Question

x^3-5x^2-14x<0

Answer 1

x^3-5x^2-14x<0

x(x^2 - 5x - 14) < 0
x(x-7)(x+2) < 0

so we have 3 critical values:
x = 0, -2, and 7

investigate each domain

1. x < -2 , I will pick x = -5
(-)(-)(-) which is < 0 , that works
2. between -2 and 0, I will pick x = -1
(-)(-1)(+) > 0 , no good
3. between 0 and 7, I will pick x = 1
(+)(-)(+) < 0 , yup, that works
4. x > 7, I will pick x = 10
(+)(+)(+) > 0 , no good

so x < -2 OR 0 < x < 7

notice I did not actually have to find the algebraic answer, just determine if the result is + or -

Answer 2

thanks!