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Math Help - Solving an inequality.

  1. #1
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    Solving an inequality.

    Hi, I must solve this inequality. How must I proceed?

    \displaystyle\frac{1}{x^2}<1

    I don't know how to, couse I cant do this: 1<x^2 so... I know its stupid, but... im a little bit stupid I think.
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  2. #2
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    Quote Originally Posted by Ulysses View Post
    Hi, I must solve this inequality. How must I proceed?

    \displaystyle\frac{1}{x^2}<1

    I don't know how to, couse I cant do this: 1<x^2 so... I know its stupid, but... im a little bit stupid I think.
    \frac{1}{x^2} < 1<br />

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

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

    critical values are x = 1 , x = -1 , and x = 0

    check the original inequality with a value from each of the four intervals defined by the critical values of x ... if the value makes the original inequality true, then all values of x in that interval make the inequality true.

    if false ... all values of x in that interval will not work.
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  3. #3
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    I've realized that I could "pass" the x^2 couse it won't change signs.

    But now I have the second derivative \displaystyle\frac{2}{x^3}>0 and I must analize its sign for the concave intervals. So, I know the solution actually, but if I proceed the same way than before I can't "pass" the x^3 couse it would change the sign.

    How should I think this?
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  4. #4
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    I'm afraid I'm not following ... what is the original problem?
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