Overview
This lecture introduces the concept of inequalities, explains inequality symbols, and demonstrates how to graph inequalities on a number line.
What Are Inequalities?
- Inequalities are mathematical statements comparing two values or expressions.
- They show that one value is greater than, less than, greater than or equal to, or less than or equal to another.
Common Inequality Symbols
- The symbol ">" means "greater than."
- The symbol "<" means "less than."
- The symbol "≥" means "greater than or equal to."
- The symbol "≤" means "less than or equal to."
- The symbol "≠" means "not equal to."
Graphing Inequalities on a Number Line
- Use an open circle on the number line for ">" and "<" to show that the number is not included.
- Use a closed circle for "≥" and "≤" to show that the number is included.
- Shade the number line to the right for ">" or "≥" and to the left for "<" or "≤".
Example Inequalities
- If x > 5, graph an open circle at 5 and shade to the right.
- If x ≤ 2, graph a closed circle at 2 and shade to the left.
Key Terms & Definitions
- Inequality — a statement comparing two values using symbols like >, <, ≥, ≤, or ≠.
- Open circle — used on a number line to indicate a value is not included.
- Closed circle — used on a number line to indicate a value is included.
Action Items / Next Steps
- Practice graphing inequalities on number lines using different symbols.
- Review the meaning and usage of each inequality symbol.