Inequality to Interval Notation Calculator
Enter your mathematical inequality using standard notation in inequality to interval notation calculator. Accepted input formats include single inequalities like x > 2, x < -3, x ≥ 0, x ≤ 5, and compound inequalities such as -3 < x < 4 or -1 ≤ x ≤ 1. The calculator also accepts reverse order like 2 < x or -3 ≥ x.
The calculator processes the inequality and converts it to interval notation.
Inequality to Interval Notation Calculator
| Inequality | Interval Notation | Description |
|---|---|---|
| x > a | (a, infinity) | Greater than a, not including a |
| x >= a | [a, infinity) | Greater than or equal to a |
| x < b | (-infinity, b) | Less than b, not including b |
| x <= b | (-infinity, b] | Less than or equal to b |
| a < x < b | (a, b) | Between a and b, not including a or b |
| a <= x <= b | [a, b] | Between a and b, including both |
| a <= x < b | [a, b) | Between a and b, including a but not b |
| a < x <= b | (a, b] | Between a and b, including b but not a |
| x != c | (-infinity, c) U (c, infinity) | All real numbers except c |
| All real numbers | (-infinity, infinity) | No restrictions on x |
Inequality to Interval Notation Formula
- x > a → (a,∞)
- x ≥ a → [a,∞)
- x < a → (-∞,a)
- x ≤ a → (-∞,a]
Parameters
- a = Lower boundary value
- b = Upper boundary value
- ( or ) = Exclusive boundary (not included)
- [ or ] = Inclusive boundary (included)
- ∞ = Infinity (always uses parentheses)
For inequality 2 < x ≤ 5: The left bound 2 < x becomes (2, the right bound x ≤ 5 becomes 5], resulting in interval notation (2,5]. For x ≥ -3, the inequality converts to [-3,∞).How to Convert Inequality to Interval Notation?
- Identify the type of inequality symbols (>, <, ≥, ≤)
- For less than (<): use parenthesis ()
- If less than or equal to (≤): use square bracket []
- For greater than (>): use parenthesis ()
- If greater than or equal to (≥): use square bracket []
- Always use parenthesis with infinity (∞)
To convert -2 ≤ x < 3, first identify the boundaries (-2 and 3) and the inequality types (≤ and <). The left inequality (≤) uses [, the right inequality (<) uses ), resulting in [-2,3).
What is Inequality and Interval Notation?
An inequality shows the relationship between expressions using special symbols (<, >, ≤, ≥). These symbols represent “less than,” “greater than,” “less than or equal to,” and “greater than or equal to.” For example, x > 3 represents all numbers greater than 3, while x ≤ 0 represents all numbers less than or equal to 0.
Interval notation is a mathematical way to represent ranges of numbers using brackets and parentheses. Square brackets [ or ] show the endpoint is included (equivalent to ≤ or ≥), while parentheses ( or ) show the endpoint is not included (equivalent to < or >). For example, [2,5] includes all numbers from 2 to 5, including both 2 and 5, while (0,∞) represents all positive numbers.