How to use
Enter one supported expression, such as −2 < x <= 5, x >= 3, 5 > x > 1, or [−2, 5). Use the variable x, decimal points, and parentheses or square brackets. Calculate shows both equivalent forms and the number line. Copy saves both forms; editing or Clear removes the previous result. The pale initial values are executable examples. Focusing or editing the first value field clears all example values once; later fields keep your own entries. Clear leaves the form empty.
Method and interpretation
A square bracket includes the endpoint; a parenthesis excludes it. Thus [2, 5) means 2 ≤ x < 5. Infinity is not a number and always takes an open parenthesis: (−inf, 3] becomes x ≤ 3. The drawing shows membership, with exact endpoint labels below it; it is a schematic, not a measurement scale.
Examples
In the inequality-to-interval direction, −2 < x <= 5 gives (−2, 5]. In the reverse direction, [1, 4) gives 1 ≤ x < 4. [3, 3] is the single point x = 3, while (3, 3] is empty. Enter R, ℝ or all for all real numbers, and ∅, {} or empty for the empty set.
Limits and errors
Only one interval or simple comparison is supported. Unions, OR, polynomials and expressions such as 2x + 1 < 5 must be solved elsewhere first. A reversed interval such as [5, 2] is an input error; contradictory inequalities such as 5 < x < 2 produce the empty set. Closed infinity brackets are rejected.
Frequently asked questions
Will close endpoints be rounded together?
No. Decimal endpoints up to 100 characters are compared exactly and keep their entered spelling. Fractions and exponent notation are not accepted. Why do two dots overlap? Equal included endpoints form a single point; any exclusion makes that interval empty.