Inequality to Interval Notation Calculator
Convert between inequality notation and interval notation with step-by-step solutions
Convert Between Notation Types
Conversion Result
Quick Reference Table
| Inequality | Interval Notation | Description |
|---|---|---|
| x > a | (a, ∞) | Greater than a |
| x ≥ a | [a, ∞) | Greater than or equal to a |
| x < a | (-∞, a) | Less than a |
| x ≤ a | (-∞, a] | Less than or equal to a |
| a < x < b | (a, b) | Between a and b (exclusive) |
| a ≤ x ≤ b | [a, b] | Between a and b (inclusive) |
| a < x ≤ b | (a, b] | Between a and b (left open) |
| a ≤ x < b | [a, b) | Between a and b (right open) |
Types of Intervals
Open Interval (a, b)
Does not include endpoints
Closed Interval [a, b]
Includes both endpoints
Half-open (a, b] or [a, b)
Includes only one endpoint
Unbounded (-∞, a) or [a, ∞)
Extends to infinity
Key Symbols
Quick Tips
Use ( ) for strict inequalities (< or >)
Use [ ] for non-strict inequalities (≤ or ≥)
Infinity symbols always use parentheses
AND operations create intersections
OR operations create unions
Understanding Interval Notation
What is Interval Notation?
Interval notation is a mathematical notation used to represent a subset of real numbers that lie between two endpoints. It provides a concise way to express the solution sets of inequalities.
Types of Brackets
- •Round brackets ( ): Exclude the endpoint (open interval)
- •Square brackets [ ]: Include the endpoint (closed interval)
- •Mixed brackets: Include one endpoint but not the other
Common Examples
Example 1:
x > 3 becomes (3, ∞)
Example 2:
-2 ≤ x < 5 becomes [-2, 5)
Example 3:
x ≤ -1 becomes (-∞, -1]
Remember: Infinity symbols (∞, -∞) always use parentheses because infinity is not a real number and cannot be included in an interval.