Nonlinear inequality

Definition

A nonlinear inequality is an inequality that involves a nonlinear expression, typically involving variables raised to powers other than one or involving products of variables. It defines a range of values that satisfy the inequality.

5 Must Know Facts For Your Next Test

1. A solution to a nonlinear inequality is a set of values that make the inequality true.
2. Graphically, solving a nonlinear inequality involves finding the regions on the coordinate plane where the inequality holds true.
3. Nonlinear inequalities can involve quadratic expressions, polynomial expressions, or other forms of non-linear functions.
4. The solution set for a nonlinear inequality can be represented using interval notation or graphical shading on a coordinate plane.
5. Systems of nonlinear inequalities involve finding common solutions that satisfy all inequalities in the system.

Review Questions

• What is the general form of a quadratic inequality?
• How do you graphically represent the solution set of $x^2 + y^2 \leq 1$?
• What methods can be used to solve systems of nonlinear inequalities?

Related terms

Quadratic Inequality: An inequality involving a quadratic expression, such as $ax^2 + bx + c \geq 0$.

Interval Notation: A way to describe sets of numbers as intervals on the real number line.

System of Equations: A set of two or more equations with the same variables; solutions must satisfy all equations simultaneously.