solution set

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

An inequality is a mathematical statement involving algebraic expressions for which we seek the values of the variables that make the inequality true. In general, an inequality between two algebraic expressions \( A(x) \) and \( B(x) \) is defined as the relation:

\[A(x) > B(x) \]

Quadratic inequalities can be interpreted geometrically by studying where the associated parabola lies above, below, or on the horizontal axis.

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:

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