This document discusses interval notation for expressing inequalities. Interval notation uses parentheses to represent < or > and brackets to represent ≤ or ≥. Inequalities can be converted to interval notation on a number line, with open or solid points indicating whether the endpoint is included or excluded. Set builder and inequality notations can also be converted to equivalent interval notation. The key aspects of interval notation covered are the symbols used and how they correspond to number lines.

1. Interval NotationExpressing Inequalities in Interval Notation

2. Notation-Inequalities < or > can be expressed using parentheses. On a number line, these symbols are noted with an OPEN pointInequalities or can be expressed using brackets. On a number line, these symbols are noted with a SOLID point.

3. Picture SummaryInequality notationInterval notation

4. ExampleInequality notationInterval notation

5. Set Builder NotationThis is read “x such that negative two is less than or equal to x is less than four.”

6. ExampleSet Builder notationInterval notation

7. Given Set Builder Notation…

8. Given Set Builder Notation…

9. Given Inequality Notation…

10. Given Inequality Notation…

11. Given Interval Notation…

12. Given Interval Notation…

13. IncreasingAs the x-values increase, the y-values also increase.Pictorially, this would appear to be a positive slope.

14. DecreasingAs the x-values increase, the y-values decrease.Pictorially, this would appear to be a negative slope.

15. ConstantAs the x-values increase, the y-values stay the same.Pictorially, this would appear to be a zero slope.

16. PositiveThe x-values for which y-values are positive.Pictorially, this would appear above the x-axis.

17. NegativeThe x-values for which y-values are negative.Pictorially, this would appear below the x-axis.

18. AssignmentBefore you leave – Check for Understanding due Assignment – “Introducing Interval Notation”