Interval Notation Examples in Math
Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Interval Notation.
This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.
Concept Recap
A shorthand for writing all real numbers in a range, using parentheses for excluded endpoints and square brackets for included endpoints.
Parentheses mean the endpoint is NOT included; square brackets mean it IS included. For example, (2, 5] means 2 < x \le 5.
Read the full concept explanation →How to Use These Examples
- Read the first worked example with the solution open so the structure is clear.
- Try the practice problems before revealing each solution.
- Use the related concepts and background knowledge badges if you feel stuck.
What to Focus On
Core idea: Interval notation encodes inequality solution sets concisely, distinguishing open endpoints from closed endpoints.
Common stuck point: Square brackets include the endpoint; parentheses exclude it. Students often swap these two symbols.
Sense of Study hint: Check each endpoint: if equal is allowed, use a square bracket; otherwise use a parenthesis.
Worked Examples
Example 1
easySolution
- 1 x > 3 means all real numbers greater than 3.
- 2 3 is not included (strict inequality), so use a parenthesis: (3.
- 3 There is no upper bound, so use \infty).
- 4 Interval: (3, \infty).
Answer
Example 2
mediumPractice Problems
Try these problems on your own first, then open the solution to compare your method.
Example 1
easyExample 2
mediumRelated Concepts
Background Knowledge
These ideas may be useful before you work through the harder examples.