Pre Calc
posted by Giselle on .
Solve the nonlinear inequality:
x^35x^214x<0

x^35x^214x<0
x(x^2  5x  14) < 0
x(x7)(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  
thanks!