Write Inequality in Interval Notation Calculator
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Reviewed by Calculator Editorial Team
This calculator helps you convert inequalities to interval notation. Interval notation is a concise way to represent sets of real numbers. It's commonly used in mathematics, science, and engineering to describe ranges of values.
How to Use This Calculator
Using our inequality to interval notation calculator is simple:
- Enter your inequality in the input field (e.g., x > 3 or -2 ≤ y < 5)
- Click the "Calculate" button
- View the interval notation result
- Review the step-by-step explanation
The calculator will convert your inequality to interval notation and provide a clear explanation of the conversion process.
Rules for Writing Inequalities in Interval Notation
When converting inequalities to interval notation, follow these key rules:
- Parentheses () indicate that an endpoint is not included in the interval
- Square brackets [] indicate that an endpoint is included in the interval
- Infinity symbols (∞) are used for unbounded intervals
- Union symbol (∪) is used to combine separate intervals
Formula: For an inequality like a < x < b, the interval notation is (a, b). For a ≤ x ≤ b, it's [a, b].
Remember that the order of the numbers in interval notation matters. The smaller number always comes first.
Examples of Inequalities in Interval Notation
Here are some common examples of inequalities written in interval notation:
| Inequality | Interval Notation | Description |
|---|---|---|
| x > 5 | (5, ∞) | All numbers greater than 5 |
| x ≤ 10 | (-∞, 10] | All numbers less than or equal to 10 |
| 3 < x < 8 | (3, 8) | All numbers between 3 and 8, not including 3 and 8 |
| 1 ≤ x ≤ 6 | [1, 6] | All numbers between 1 and 6, including both endpoints |
| x < -2 or x > 4 | (-∞, -2) ∪ (4, ∞) | All numbers less than -2 or greater than 4 |
These examples demonstrate how to convert different types of inequalities to interval notation using the proper symbols and syntax.
Frequently Asked Questions
What is interval notation?
Interval notation is a way to represent a set of real numbers using intervals on the number line. It uses parentheses () for open intervals and square brackets [] for closed intervals.
How do I know when to use parentheses or brackets?
Use parentheses () when the endpoint is not included in the interval (strict inequality). Use square brackets [] when the endpoint is included (non-strict inequality).
What does the ∪ symbol mean in interval notation?
The ∪ symbol (union) is used to combine two separate intervals. For example, (-∞, -2) ∪ (4, ∞) represents all numbers less than -2 or greater than 4.
Can I use interval notation for inequalities with more than one variable?
Yes, you can use interval notation for inequalities with multiple variables, but you would need to specify the interval for each variable separately.