Inequality

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

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

Thanks,
Armando

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  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

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