# Solve inequality of fraction in terms of denominator variable

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.

## 1 Answer

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:

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

• Thanks, can't say that I get it, maybe you can reference me what to read to improve my knowledges in it? – Oleg Dec 16 '18 at 11:37
• I honestly wouldn't know myself; this is a fairly basic technique taught in your typical algebra class in elementary or middle school. So I guess some textbook of the sort, or perhaps some videos on Khan Academy might help? (Not sure if Khan Academy covers this particular topic but I'm pretty sure they have pretty much everything from the standard K-12 math curriculum on their site.) – Eevee Trainer Dec 16 '18 at 11:39
• I got it, thanks. – Oleg Dec 16 '18 at 12:05