Writing and Graphing Inequalities

This page introduces the concept of inequalities and how they differ from expressions and equations. It explains how to graph inequalities on a number line and interpret their solutions.

Definition: An inequality is a mathematical statement that compares two expressions using inequality symbols (<, >, ≤, ≥).

The page illustrates the differences between expressions, equations, and inequalities:

1. Expression $e.g., 5x+2$: This is a combination of numbers and variables without an equal sign.

2. Equation $e.g., 5x+2=12 or x=3$: These have a single, specific solution.

Example: In the equation x=3, x can only be 3.

3. Inequality $e.g., x≤-2 or x>3$: These have multiple solutions.

Example: In the inequality x>3, x can be 3 or any number greater than 3.

The page also explains how to graph inequalities on a number line:

• For inequalities including the equal sign (≤ or ≥), use a closed dot on the number line.
• For strict inequalities (< or >), use an open dot on the number line.

Highlight: When graphing x≤-2, use a closed dot at -2 because -2 is included in the solution set.

Vocabulary:

• Closed Dot: Used when the endpoint is included in the solution set (≤ or ≥).
• Open Dot: Used when the endpoint is not included in the solution set (< or >).

This introduction to writing and graphing inequalities provides a foundation for more advanced topics in algebra and helps students visualize the solution sets of inequalities.