JAMB 1994 · UME · Q17

Find the range of values of $x$ for which $\frac1x > 2$ is true.

Worked solution (try it first)

If $x$ were negative, $\frac1x$ would be negative and could not be greater than 2.
So $x > 0$ .
With $x$ positive, multiply both sides by $x$ without reversing the sign: $1 > 2x$ , so $x < \frac12$ .
Put the two together: $0 < x < \frac12$ , option C.