Turn Inequality to Interval Notation Calculator

How to Use This Calculator

Using our inequality to interval notation calculator is straightforward. Follow these 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 (usually x or y).
3. Click the "Calculate" button to convert the inequality to interval notation.
4. Review the result and the step-by-step explanation provided.

The calculator will display the interval notation and explain how it was derived from your inequality.

Conversion Rules

Converting inequalities to interval notation involves understanding the symbols and their meanings. Here are the basic rules:

• Greater than (>) and less than (<): These symbols are converted to parentheses in interval notation. For example, x > 3 becomes (3, ∞).
• Greater than or equal (≥) and less than or equal (≤): These symbols are converted to brackets in interval notation. For example, x ≥ 3 becomes [3, ∞).
• Compound inequalities: When an inequality has both a lower and upper bound, such as 1 < x < 5, it becomes (1, 5). If the bounds are inclusive, use brackets: 1 ≤ x ≤ 5 becomes [1, 5].

Examples

Let's look at a few examples to illustrate how to convert inequalities to interval notation.

Example 1: Simple Inequality

Inequality: x > 4

Interval Notation: (4, ∞)

Explanation: The inequality x > 4 means all numbers greater than 4. In interval notation, we use a parenthesis to indicate that 4 is not included.

Example 2: Inclusive Inequality

Inequality: y ≤ 7

Interval Notation: (-∞, 7]

Explanation: The inequality y ≤ 7 includes all numbers less than or equal to 7. We use a bracket to show that 7 is included.

Example 3: Compound Inequality

Inequality: 2 < x ≤ 10

Interval Notation: (2, 10]

Explanation: This inequality includes all numbers greater than 2 and less than or equal to 10. We use a parenthesis for the lower bound (not included) and a bracket for the upper bound (included).

Common Pitfalls

When converting inequalities to interval notation, there are a few common mistakes to avoid:

• Mixing parentheses and brackets: Remember that parentheses indicate that the endpoint is not included, while brackets indicate that it is included. Mixing them up can lead to incorrect interval notation.
• Incorrect order of bounds: Always write the lower bound first, followed by the upper bound. For example, (1, 5) is correct, while (5, 1) is not.
• Forgetting infinity: When an inequality has no upper or lower bound, use the infinity symbol. For example, x > 3 becomes (3, ∞), not (3, ).