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Enter your inequality to see the correct interval notations with step-by-step explanation.
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This Interval Notation Calculator helps you convert mathematical inequalities into proper interval notation easily. Whether you're a student learning algebra, a teacher explaining number systems, or a math enthusiast, this tool allows you to represent solution sets and numerical ranges accurately. It clearly explains the meaning of every bracket, parenthesis, and infinity symbol, helping you avoid mistakes and understand interval notation better.
Interval notation is a mathematical method used to describe a continuous range of numbers on a number line. Instead of writing inequalities in long form, interval notation offers a compact and readable format.
For example, the inequality 2 ≤ x < 5 can be written as [2, 5). The symbols indicate whether endpoints are included or excluded:
Interval notation is commonly used to describe domains, ranges, and solution sets in algebra and calculus, simplifying real number set representation and improving readability.
Interval notation provides a concise way to represent inequalities and continuous numerical ranges. It is especially helpful for:
Using an interval notation calculator reduces errors and saves time, particularly when working with infinity or multiple inequalities.
Let’s go through an example to convert an inequality into interval notation.
Example:
Convert the inequality 7 - x/6 > 8 into interval notation:
7 - x 6 > 8
Subtract 7 from both sides:
- x 6 > 1
Multiply both sides by -1 and reverse the inequality sign:
x 6 < -1
Multiply both sides by 6:
x < -6
Since x is less than -6, the interval notation is:
(-∞, -6)
Result Interpretation:
Intervals are classified based on whether their endpoints are included or excluded:
An open interval does not include its endpoints. For example, {x | 2 < x < 5} is written as (2, 5).
A closed interval includes both endpoints. For example, {x | 2 ≤ x ≤ 5} is written as [2, 5].
A half-open interval includes one endpoint and excludes the other. For example, {x | 2 ≤ x < 5} is written as [2, 5).
The interval notation representing all real numbers is:
(-∞, ∞)
Wikipedia: Interval (Mathematics)
Brilliant: Writing Interval Notation
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