Solve inequality of fraction in terms of denominator variable

Question

I have such inequality:

$$-0.1b \le \frac{y}{x} \le 0.1b$$

How to solve it in terms of x to have something like this:

$$ ? \le x \le ? $$

Thanks for any help.

Answer 1

You'd take the reciprocal of each term in the inequality, then multiply each term by $y$.

Note, however, taking the reciprocal reverses the order of the inequality symbols. For example, notice:

$$1 < 2 < 3 \;\;\; \Leftrightarrow \;\;\; 1 > \frac{1}{2} > \frac{1}{3}$$