Nonlinear Inequalities

Nonlinear inequalities involve expressions where variables are raised to powers other than one, multiplied, divided, or combined in ways that produce curves or complex shapes when graphed. Unlike linear inequalities, which form straight lines, nonlinear inequalities can produce circles, parabolas, or other curves. Solving them involves determining the set of all variable values that satisfy the inequality, often requiring techniques like testing regions, factoring, or graphing. They are essential in describing real-world situations where relationships are not straightforward, such as in physics, economics, or biology, where interactions often produce curved or complex patterns.