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

What is 'Case Analysis' ??

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- Oct 2nd 2008, 06:16 AMrednestHelp: Case analysis
Solve the inequality $\displaystyle \frac{1}{x}<x<1$ by Case Analysis.

What is 'Case Analysis' ?? - Oct 2nd 2008, 07:29 AMPlato
Consider two cases:

Case I. $\displaystyle x>0$ and then solve.

Case II. $\displaystyle x<0$ annd then sove. - Oct 2nd 2008, 10:40 AMShowcase_22
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.

$\displaystyle \frac{1}{x}<x<1$

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

$\displaystyle 1>x^2>x$

Then solve each separate equation:

$\displaystyle 1>x^2$ and $\displaystyle x^2>x$.

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

Hope it helps!