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Math Help - Inequalities

  1. #1
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    Inequalities

    \frac 1{3x^2-x-2}<0

    I understand that in algebra inequalities one side has to be made zero but in the equation shown above, I am unable to find the set of values that satisfies the equation.
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Air View Post
    \frac 1{3x^2-x-2}<0

    I understand that in algebra inequalities one side has to be made zero but in the equation shown above, I am unable to find the set of values that satisfies the equation.
    well, we know that < 0 means it is negative, correct? and if the numerator of a fraction is positive, the only way to make it negative is if we make the denominator negative.

    now, 1 is a positive number, therefore, to make the fraction \frac {1}{3x^2 - x - 2} < 0, we must have that 3x^2 - x - 2 < 0

    so now, your problem is actually to solve this last inequality. treat the < sign as an equal sign at first and solve (you keep writing "<" but treat it as if it were "="); then make sure the interval solutions you choose for your x-values make the solution set negative.
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