Hi, can someone explain how to solve this inequality...

Question

2x^3 - 7x^2 < 8x - 28

Thanks,
Armando

Answer 1

2x^3 - 7x^2 < 8x - 28
2x^3 - 7x^2 - 8x + 28 < 0

after some quick trials, I found 2 and -2 to be roots of the corresponding equation
so it factors to
(x+2)(x-2)(2x-7) < 0

so critical values are 2 , -2, and 3.5

Knowing the typical appearance of a cubic with a positive cube terms, it can be shown that the expression is negative (<0) for all values between +2 and 3.5 as well as all values of x < -2

so

x < -2 OR 2 < x < 3.5