how solve the inequality $−1\leq \leq1$? How can we solve this equation graphically ? why we talk about the two hyperbole $\frac{1}{x}$ and $\frac{-1}{x}$ ?
I divided this equation on two sub-equations $$ xy\leq1$$ and  $$xy\geq-1$$.
For the first sub-equation  I have two cases when x is greater or not than zero. Also for the second I have two other equations depending if $x \geq0$ or not.
That said, I no longer know how to solve my system of 4 sub equations

Dividing by cases, we have that

*

*for $x>0$
$$−1\leq \leq1 \iff -\frac1x \le y \le \frac1x$$

*

*for $x<0$ (direction of inequalities flip)

$$−1\leq \leq1 \iff \frac1x \le y \le -\frac1x$$
and for $x=0 \implies xy=0$.
