Inequality Calculator in Interval Notation
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Reviewed by Calculator Editorial Team
This inequality calculator helps you convert mathematical inequalities to interval notation. Learn how to solve and graph inequalities in interval notation with our step-by-step guide and examples.
What is Interval Notation?
Interval notation is a way to represent a set of real numbers using a pair of numbers and parentheses or brackets. It's commonly used in calculus, algebra, and other branches of mathematics to describe ranges of values.
There are four main types of intervals:
- Open interval: (a, b) - includes all numbers between a and b, but not a and b themselves
- Closed interval: [a, b] - includes all numbers between a and b, including a and b
- Half-open interval: (a, b] or [a, b) - includes one endpoint but not the other
- Infinite interval: (a, ∞), [-∞, b], or [-∞, ∞] - represents all numbers greater than a, less than b, or all real numbers
Interval notation is particularly useful when dealing with inequalities because it provides a clear and concise way to represent the solution set.
How to Convert Inequalities to Interval Notation
Converting inequalities to interval notation involves following these steps:
- Solve the inequality to find the range of values that satisfy it
- Identify the endpoints of the interval
- Determine whether the endpoints are included or excluded
- Write the interval in the appropriate notation
Example: Convert the inequality -3 ≤ x < 5 to interval notation.
Solution: The inequality includes all numbers from -3 up to but not including 5. In interval notation, this is written as [-3, 5).
Special Cases
When dealing with inequalities that involve infinity or no solution, you'll need to use special interval notation:
- x > 3 becomes (3, ∞)
- x ≤ -2 becomes (-∞, -2]
- No solution becomes the empty set, represented as ∅ or an empty interval ()
Examples of Inequality to Interval Notation
Let's look at several examples to see how inequalities are converted to interval notation:
| Inequality | Interval Notation | Graph |
|---|---|---|
| -2 < x ≤ 4 | (-2, 4] | •••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• |