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Turn Inequality Into Interval Notation Calculator

Reviewed by Calculator Editorial Team

This calculator helps you convert mathematical inequalities into interval notation, which is commonly used in algebra and calculus. Whether you're a student studying number lines or a professional working with mathematical expressions, this tool provides a quick and accurate way to perform the conversion.

How to Use This Calculator

Using our inequality to interval notation calculator is straightforward. Follow these simple steps:

  1. Enter your inequality in the input field. For example, you might enter x > 3 or -2 ≤ y < 5.
  2. Select the variable you're solving for from the dropdown menu.
  3. Click the "Calculate" button to convert the inequality to interval notation.
  4. Review the result, which will be displayed in both interval notation and a graphical representation.

The calculator will handle all the conversion work for you, showing you the proper interval notation and explaining how it was derived.

The Conversion Process

Converting an inequality to interval notation involves several steps. Here's how it works:

  1. Identify the inequality: Start with an inequality like x > 3 or -2 ≤ y < 5.
  2. Determine the variable: Identify which variable you're solving for (usually x or y).
  3. Convert to interval notation: Use the following rules:
    • a < x < b becomes (a, b)
    • a ≤ x ≤ b becomes [a, b]
    • x > a becomes (a, ∞)
    • x ≥ a becomes [a, ∞)
    • x < b becomes (-∞, b)
    • x ≤ b becomes (-∞, b]
  4. Write the final notation: Combine the intervals using the appropriate brackets and infinity symbols.

Formula: The conversion follows standard mathematical notation rules for intervals.

For example, the inequality 2 < x ≤ 7 converts to the interval notation (2, 7].

Worked Examples

Example 1: Simple Inequality

Convert x > 4 to interval notation.

  1. Identify the inequality: x > 4
  2. Determine the variable: x
  3. Convert to interval notation: (4, ∞)

The interval notation for x > 4 is (4, ∞).

Example 2: Compound Inequality

Convert -3 ≤ y < 2 to interval notation.

  1. Identify the inequality: -3 ≤ y < 2
  2. Determine the variable: y
  3. Convert to interval notation: [-3, 2)

The interval notation for -3 ≤ y < 2 is [-3, 2).

Frequently Asked Questions

What is interval notation?

Interval notation is a way of representing sets of real numbers using parentheses and square brackets. Parentheses indicate that an endpoint is not included, while square brackets indicate that an endpoint is included.

How do I convert an inequality to interval notation?

To convert an inequality to interval notation, identify the variable and the range it covers. Use parentheses for strict inequalities and square brackets for inclusive inequalities. Combine the intervals using the appropriate symbols.

What does the infinity symbol represent in interval notation?

The infinity symbol (∞) in interval notation represents all numbers extending to infinity in the positive or negative direction, depending on the context.

Can I use this calculator for inequalities with more than one variable?

This calculator is designed for inequalities with a single variable. For inequalities with multiple variables, you would need to solve for one variable at a time.