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Math Help - Help: Case analysis

  1. #1
    Junior Member rednest's Avatar
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    Help: Case analysis

    Solve the inequality \frac{1}{x}<x<1 by Case Analysis.

    What is 'Case Analysis' ??
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  2. #2
    MHF Contributor

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    Consider two cases:
    Case I. x>0 and then solve.

    Case II. x<0 annd then sove.
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  3. #3
    Super Member Showcase_22's Avatar
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    Have you noticed that on MA132 Foundations Exercises 1 there's a typo in Section A? 1 ii) doesn't make sense!

    Anyway, plato was right with what he posted.

    Remember to flip the inequality sign around when you take s as a negative.

    \frac{1}{x}<x<1

    If x is negative then multiply through by x and flip the signs around:

    1>x^2>x

    Then solve each separate equation:

    1>x^2 and x^2>x.

    When x is positive, just solve 1<x^2<x by splitting it into two separate inequalities like above.

    Hope it helps!
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