systems of inequalities

Inequalities are mathematical statements comparing expressions by order relations, whose solutions are values or intervals that make the relation true.

A system of inequalities is a set of at least two inequalities involving one or more variables, for which we seek the values of the variables that simultaneously satisfy all the inequalities. These systems have the general form:

\[
\begin{cases}
f_1(x) \, \text{relation} \, 0 \\[0.5em]
f_2(x) \, \text{relation} \, 0 \\[0.5em]
\quad \quad \quad \vdots \\[0.5em]
f_k(x) \, \text{relation} \, 0
\end{cases}
\]