Interval Notation: A way to represent intervals using parentheses and brackets.
Parentheses: Indicates that the endpoint is not included.
Brackets: Indicates that the endpoint is included.
Infinity (∞): Always associated with parentheses.
Open Circle: Endpoint not included.
Closed Circle: Endpoint included.
Examples
1. x > 4
Number Line: Open circle at 4, shade to the right.
Interval Notation: (4, ∞)
2. x ≥ 2
Number Line: Closed circle at 2, shade to the right.
Interval Notation: [2, ∞)
3. x < 3
Number Line: Open circle at 3, shade to the left.
Interval Notation: (-∞, 3)
4. x ≤ -1
Number Line: Closed circle at -1, shade to the left.
Interval Notation: (-∞, -1]
Compound Inequalities
5. 2 < x ≤ 6
Number Line: Open circle at 2, closed circle at 6, shade between.
Interval Notation: (2, 6]
6. -3 ≤ x < 4
Number Line: Closed circle at -3, open circle at 4, shade between.
Interval Notation: [-3, 4)
7. x < -2 or x ≥ 5
Number Line:
Open circle at -2, shade to the left.
Closed circle at 5, shade to the right.
Interval Notation: (-∞, -2) ∪ [5, ∞)
8. x ≤ 1 or x > 2
Number Line:
Closed circle at 1, shade to the left.
Open circle at 2, shade to the right.
Interval Notation: (-∞, 1] ∪ (2, ∞)
Conclusion
Always graph the solution on a number line first.
Translate the number line into interval notation using the appropriate symbols for open and closed circles and intervals including or excluding endpoints.