Inleiding tot niet-lineaire ongelijkheden

In the linear inequality, the boundary describes a straight line that separates the solution region from the region that satisfies the other condition of the inequality.

In contrast, a nonlinear inequality involves higher-degree expressions and defines regions using curved boundaries instead of straight lines.

When working with such inequalities—particularly polynomial types—solutions are often found by factoring the expression and setting each factor equal to zero to determine the roots, or zeros.

These points are not included in the solution but indicate where the expression changes sign, dividing the number line into intervals that can be tested for validity within the inequality.

A value from each interval is substituted into the original inequality to determine whether the expression holds true in that region.

The intervals where the inequality is satisfied define the solution regions.

In a business context, profit is the difference between revenue and the cost of units sold. To ensure a profit of at least 20 dollars, the condition is expressed as a nonlinear inequality. Solving this inequality gives the specific range of units for which the profit requirement is satisfied.