Inequality

Definition

Inequality is a mathematical statement that shows the relationship between two expressions that are not equal. It often involves symbols like $\lt$, $\leq$, $\gt$, or $\geq$.

5 Must Know Facts For Your Next Test

1. An inequality can be linear or nonlinear, depending on the degree of the variables involved.
2. Graphing inequalities in two variables involves shading a region of the coordinate plane.
3. Systems of inequalities can have multiple solutions forming a solution set, often represented as a shaded area where all conditions are satisfied.
4. To solve systems of nonlinear inequalities, you may need to use methods such as substitution or elimination.
5. Boundary lines for inequalities are drawn dotted for strict inequalities (e.g., $<$ or $>$) and solid for inclusive inequalities (e.g., $\leq$ or $\geq$).

Review Questions

• What is the difference between a strict inequality and an inclusive inequality?
• How do you graph a system of nonlinear inequalities?
• What methods can be used to solve systems of nonlinear inequalities?

Related terms

Linear Inequality: An inequality involving linear expressions, such as $ax + by \lt c$.

System of Equations: A set of equations with multiple variables that are solved together.

Solution Set: The set of all values that satisfy a given system of equations or inequalities.