Interval notation is a compact way to write sets of real numbers: square brackets include an endpoint, round brackets exclude it, and infinity always gets a round bracket. It is the standard way to state domains, ranges and solution sets.
How to use the Inequality to Interval Notation Calculator
- Conversion type
- Inequality type
- Inequality
- Interval
- a
- Left end
- Right end
- b
Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.
How it works
Choose whether the inequality is one-sided or two-sided, pick the signs and enter the endpoints. The calculator writes the interval, the inequality and the set-builder form.
Formula
x < a → (−∞, a) x ≤ a → (−∞, a] a ≤ x < b → [a, b)
Worked example
Inputs — Conversion type: Inequality → interval; Inequality type: Two-sided (a … x … b); a: -2; Left end: a ≤ x (closed); Right end: x < b (open); b: 5.
Results — Result = [−2, 5); Set-builder form = [−2, 5) = {x | −2 ≤ x < 5}; The other notation = −2 ≤ x < 5.
Key terms
- Open interval
- (a, b), excluding both endpoints.
- Closed interval
- [a, b], including both endpoints.
Frequently asked questions
How do I write x > 3 in interval notation?
(3, ∞).
How do I write −1 ≤ x ≤ 4?
[−1, 4].
Why is infinity never in a square bracket?
Infinity is not a number, so it cannot be included in the set.
How do I write "all real numbers"?
(−∞, ∞).