Inequality to Interval Notation Converter

Learn Interval Notation

Interval notation is a way to represent sets of real numbers. It's commonly used to express the solutions to inequalities. Instead of writing inequalities like \(x < 5\) or \(x \geq -2\), we use parentheses and brackets to denote intervals.

• Parentheses \((\,)\) indicate that the endpoint is not included in the interval (open interval). For example, \( (a, b) \) represents all numbers between \(a\) and \(b\), excluding \(a\) and \(b\).
• Brackets \([\,]\) indicate that the endpoint is included in the interval (closed interval). For example, \( [a, b] \) represents all numbers between \(a\) and \(b\), including \(a\) and \(b\).
• We use \(-\infty\) and \(\infty\) to represent intervals that extend indefinitely to the left or right. Infinity is always enclosed in parentheses because it's not a number and cannot be included.

Examples:

• \( x < 5 \) is written as \( (-\infty, 5) \)
• \( x ≤ -2 \) is written as \( (-\infty, -2] \)
• \( x > 3 \) is written as \( (3, \infty) \)
• \( x ≥ 0 \) is written as \( [0, \infty) \)
• \( -1 < x ≤ \) is written as \( (-1, 4] \)

This tool helps you convert inequalities into interval notation and visualize them on a number line, making it easier to understand the range of values that satisfy the inequality.

Learn more about interval notation on resources like Math is Fun or Wikipedia.