Example 15. Solve the system of inequalities

$$
\left\{\begin{array}{l}
|2 x-3| \leqslant 3 \\
\frac{1}{x}<1
\end{array}\right.
$$
Solution. The domain of the system consists of all real numbers except zero. The first inequality of the system is equivalent to the double inequality

$$
-3 \leqslant 2 x-3 \leqslant 3 \Leftrightarrow 0 \leqslant 2 x \leqslant 6 \Leftrightarrow 0 \leqslant x \leqslant 3
$$

If $x>0$, then the inequality $1 / x < 1$.

Thus, the solution set of the system consists of all $x$ in the interval ( $1 ; 3]$.

To solve an inequality with two unknowns $x$ and $y$ means to find all ordered pairs of numbers ( $x, y$ ), which, when substituted into the given inequality, result in a true numerical inequality.