Inequality

Definition

An inequality is a mathematical statement that indicates the relative size or order of two values using symbols such as <, >, ≤, or ≥. Inequalities can be solved to find the range of values that satisfy the given conditions.

5 Must Know Facts For Your Next Test

1. Inequalities can be represented graphically on a coordinate plane, with the solution region often being a shaded area.
2. When solving inequalities involving two variables, you may need to test points to determine which regions satisfy the inequality.
3. Nonlinear inequalities involve terms like quadratics ($x^2$), cubics ($x^3$), or other polynomial expressions.
4. Systems of inequalities consist of multiple inequalities that are considered simultaneously, and their solutions are typically found in overlapping regions on a graph.
5. The boundary line of an inequality can be solid (for ≤ or ≥) or dashed (for < or >), indicating whether points on the line are included in the solution set.

Review Questions

• How do you determine whether to use a solid or dashed boundary line when graphing an inequality?
• What methods can be used to solve a system of nonlinear inequalities?
• How do you identify the solution region for a system of inequalities involving two variables?

Related terms

System of Equations: A collection of two or more equations with a common set of variables.

Quadratic Equation: An equation where the highest exponent of the variable is squared (e.g., $ax^2 + bx + c = 0$).

Boundary Line: The line corresponding to an equality within an inequality; it divides the coordinate plane into regions.