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Inequality

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College Algebra

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.

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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?

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