Inequality Notation to Interval Notation Calculator

Calculator

Example Data Table

Formula Used

This calculator follows interval notation rules for real numbers.

• Use ( ) when an endpoint is not included.
• Use [ ] when an endpoint is included.
• Use -∞ or ∞ with parentheses only.
• Use ∪ when the solution has separate parts.
• Translate x > a into (a, ∞).
• Translate x >= a into [a, ∞).
• Translate x < b into (-∞, b).
• Translate x <= b into (-∞, b].
• Translate a < x < b into (a, b).
• Translate a <= x <= b into [a, b].

How to Use This Calculator

1. Type the inequality in the input box.
2. Enter the variable symbol if needed.
3. Choose the number of decimal places.
4. Select whether to show steps and summary text.
5. Click the convert button.
6. Read the interval notation shown above the form.
7. Download the result as CSV or PDF if needed.

Inequality Notation to Interval Notation Guide

Why this conversion matters

Inequality notation and interval notation describe the same solution set. They just look different. Students often move between both forms in algebra, graphing, and calculus. A quick converter saves time. It also reduces bracket mistakes.

How interval notation works

Interval notation uses parentheses and brackets. Parentheses show an endpoint is excluded. Brackets show an endpoint is included. Infinite endpoints always use parentheses. This is because infinity is never an actual endpoint value.

Reading simple inequalities

A simple inequality has one comparison. For example, x > 4 means every value larger than 4. The correct interval is (4, ∞). If the inequality is x >= 4, the interval becomes [4, ∞). That bracket shows 4 belongs to the set.

Reading compound inequalities

Compound inequalities have two comparisons. For example, 2 < x < 9 becomes (2, 9). If one sign includes equality, the matching side uses a bracket. So 2 <= x < 9 becomes [2, 9). This detail matters in test answers.

Working with unions

Some inequalities create two separate intervals. A common example is x != 3. The solution is every real number except 3. Interval notation writes that as (-∞, 3) ∪ (3, ∞). The union symbol joins solution pieces together.

Common errors to avoid

Many learners mix up brackets and parentheses. Others place brackets next to infinity. That is never correct. Another mistake is forgetting that “or” statements often create unions. This calculator helps spot those cases and shows each step clearly.

Best use cases

Use this inequality notation to interval notation calculator for homework checks, lesson planning, worksheets, and quick revision. It works well for simple inequalities, compound ranges, and exclusions. The included examples, steps, and exports make the page practical for daily math work.

FAQs

1. What is interval notation?

Interval notation is a compact way to show sets of real numbers. It uses brackets for included endpoints and parentheses for excluded endpoints.

2. When do I use brackets?

Use brackets when the endpoint is included in the solution. This happens with ≤ or ≥ and with exact endpoint values inside a closed interval.

3. When do I use parentheses?

Use parentheses when the endpoint is excluded. This happens with < or >. Infinity also always uses parentheses.

4. How is x > 5 written?

x > 5 becomes (5, ∞). The 5 is excluded, so the left side is open.

5. How is 2 <= x < 8 written?

It becomes [2, 8). The 2 is included, while 8 is not included.

6. What does the union symbol mean?

The union symbol joins separate solution parts. It is used when one inequality produces multiple intervals, such as x != 4.

7. Can this page handle compound inequalities?

Yes. It reads many compound forms, including double inequalities and basic OR statements with separate interval pieces.

8. Why can infinity not use brackets?

Infinity is not a real endpoint value. Because it cannot be included, interval notation always places infinity inside parentheses.