Inequalities Interval Notation Calculator

This calculator converts inequalities to interval notation. Interval notation is a concise way to represent sets of real numbers using parentheses and brackets. It's commonly used in mathematics, engineering, and science to describe ranges of values.

How to Use This Calculator

To convert an inequality to interval notation:

Enter your inequality in the input field (e.g., x > 3 or -2 ≤ y < 5)
Select the variable you're solving for (x, y, or z)
Click "Calculate" to see the interval notation result
Review the step-by-step conversion process

The calculator will display the interval notation, a visual representation of the interval, and an explanation of the conversion process.

Conversion Rules

Here are the basic rules for converting inequalities to interval notation:

Inequality Symbol	Interval Notation Symbol	Meaning
>	(	Parentheses indicate the endpoint is not included
<	)	Parentheses indicate the endpoint is not included
≥	[	Brackets indicate the endpoint is included
≤	]	Brackets indicate the endpoint is included

Formula

For an inequality of the form a < x < b, the interval notation is (a, b).

For a ≤ x ≤ b, the interval notation is [a, b].

For x > a, the interval notation is (a, ∞).

For x ≥ a, the interval notation is [a, ∞).

Examples

Example 1: Simple Inequality

Inequality: 2 < x < 8

Interval Notation: (2, 8)

Explanation: The parentheses indicate that x is greater than 2 and less than 8, but not equal to either endpoint.

Example 2: Inclusive Endpoints

Inequality: -3 ≤ y ≤ 10

Interval Notation: [-3, 10]

Explanation: The brackets indicate that y can be equal to -3 and 10, in addition to all values between them.

Example 3: One-Sided Inequality

Inequality: z > -5

Interval Notation: (-5, ∞)

Explanation: The interval extends to infinity with an open parenthesis since z cannot be equal to -5.

Common Errors

When converting inequalities to interval notation, these are common mistakes to avoid:

Using the wrong bracket type - remember that parentheses () indicate exclusion while brackets [] indicate inclusion
Mixing up the order of endpoints - always write the smaller number first
Forgetting to include infinity (∞) for one-sided inequalities
Using the wrong inequality symbol when converting back to standard form

Tip

Double-check your work by converting the interval notation back to inequality form to ensure accuracy.

FAQ

What is interval notation?

Interval notation is a way to represent sets of real numbers using parentheses and brackets. It's a concise method that's widely used in mathematics, engineering, and science.

How do I know when to use parentheses vs. brackets?

Use parentheses () when the endpoint is not included (strict inequality) and brackets [] when the endpoint is included (non-strict inequality).

What does ∞ mean in interval notation?

Infinity (∞) represents all numbers greater than any finite number. It's used in interval notation to indicate that one endpoint of the interval extends infinitely.

Can I use interval notation for inequalities with more than one variable?

Interval notation is typically used for inequalities with a single variable. For multiple variables, you would need to consider each variable separately or use a different notation system.