Inequality To Interval Notation

Q: What is the difference between parentheses and brackets in interval notation?

In interval notation, parentheses ( ) indicate that the endpoint is NOT included (strict inequality ), while brackets [ ] indicate the endpoint IS included (>= or 3 gives (3, ∞), while x >= 3 gives [3, ∞).

Q: Is this inequality to interval notation tool free?

Yes, all calculators on Calculy are completely free to use with no registration or downloads required.

Q: Can I convert inequalities with variables on both sides?

This calculator converts simple inequalities directly to interval notation. For more complex inequalities with variables on both sides, simplify the inequality first to the forms supported here (x > a, etc.) before using the tool.

Convert any inequality (x>a, x<=b, a<x<b, etc.) to interval notation instantly. Choose from 8 types and get the matching interval with number line visual.

Convert to interval

Inequality Type:

Bound a:

About This Calculator

The Inequality to Interval Notation calculator converts any inequality statement into its corresponding interval notation form. Interval notation is a concise way to represent sets of real numbers using parentheses (for strict inequalities) and brackets (for inclusive inequalities).

This tool is essential for algebra and precalculus students learning to express solution sets, as well as anyone working with inequalities in mathematics. Select from 8 common inequality types including single inequalities (x > a, x >= a, x < a, x <= a) and compound/between inequalities (a < x < b, a <= x <= b, a <= x < b, a < x <= b). Enter the numerical bounds and get the interval notation, the original inequality, and a visual number line representation showing open (◯) and closed (●) endpoints.

Examples: x greater than 3 becomes (3, ∞). x up to -2 becomes (-∞, -2]. x between -1 and 5 becomes (-1, 5). x from 0 through 10 becomes [0, 10].

Frequently Asked Questions

What is the difference between parentheses and brackets in interval notation?

In interval notation, parentheses ( ) indicate that the endpoint is NOT included (strict inequality < or >), while brackets [ ] indicate the endpoint IS included (>= or <=). For example, x > 3 gives (3, ∞), while x >= 3 gives [3, ∞).

Why is infinity always written with a parenthesis?

Infinity (∞) is not a real number -- it represents an unbounded direction. Since you cannot reach infinity, it can never be included as an endpoint. Therefore, ∞ always gets a parenthesis, never a bracket.

What are the 8 supported inequality types?

The calculator supports x > a, x >= a, x < a, x <= a, a < x < b, a <= x <= b, a <= x < b, and a < x <= b. These cover all standard single and compound inequalities taught in algebra.

Is this inequality to interval notation tool free?

Yes, all calculators on Calculy are completely free to use with no registration or downloads required.

Can I convert inequalities with variables on both sides?

This calculator converts simple inequalities directly to interval notation. For more complex inequalities with variables on both sides, simplify the inequality first to the forms supported here (x > a, etc.) before using the tool.

What does the number line representation show?

The number line representation uses ● for included endpoints (brackets) and ◯ for excluded endpoints (parentheses). Arrows show the direction of the interval. For example, x >= 2 is shown as ●------ 2 ->, and x < 5 as <- ------ 5 ◯.