Overview
This lecture introduces the basics of inequalities, explains the meaning of different inequality symbols, and demonstrates how to represent inequalities on a number line.
Inequality Symbols
- The "<" symbol means "less than" (e.g., x < 10 means x is any number less than 10).
- The ">" symbol means "greater than" (e.g., x > 10 means x is any number greater than 10).
- The "ā¤" symbol means "less than or equal to" (e.g., x ā¤ 10 means x is 10 or less).
- The "ā„" symbol means "greater than or equal to" (e.g., x ā„ 10 means x is 10 or greater).
- The less than sign (ā<ā) resembles an "L" to help remember its meaning.
- An inequality can be rewritten by reversing the expression and the symbol (e.g., x < 10 is the same as 10 > x).
Working with Negative Numbers and Compound Inequalities
- Inequalities work with negative numbers (e.g., x < -5 means x is any number less than -5).
- x ā„ -5 means x is -5 or any number greater than -5.
- Compound inequalities use two signs (e.g., 3 < x ā¤ 7 means x is greater than 3 and less than or equal to 7).
- For whole numbers, 3 < x ā¤ 7 limits x to 4, 5, 6, or 7.
Representing Inequalities on a Number Line
- Use circles to mark boundary points on the number line.
- Fill in the circle if the value is included ("ā¤" or "ā„"); leave it empty if not ("<" or ">").
- Connect the circles with a line to show the range of possible values.
- Example: For -3 ā¤ x < 4, fill in the circle at -3, leave the circle at 4 empty, and join them with a line.
Key Terms & Definitions
- Inequality ā a mathematical statement indicating that one value is larger or smaller than another.
- Number line ā a visual representation of numbers on a straight line to show value ranges.
- Compound inequality ā an expression with two inequality signs showing a range for a variable.
Action Items / Next Steps
- Practice drawing inequalities on number lines using different symbols and ranges.