Solve the inequality $\displaystyle \frac{1}{x}<x<1$ by Case Analysis.
What is 'Case Analysis' ??
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!