Calculator
Supported forms include simple, compound, reverse, equal, not equal, and union inequalities.
Example Data Table
| Inequality Input | Interval Notation | Meaning |
|---|---|---|
| x > 4 | (4, ∞) | All values greater than 4 |
| x <= 9 | (-∞, 9] | All values up to and including 9 |
| 2 < x < 7 | (2, 7) | Values strictly between 2 and 7 |
| -3 <= x < 5 | [-3, 5) | Closed left endpoint and open right endpoint |
| x != 1 | (-∞, 1) ∪ (1, ∞) | All real numbers except 1 |
| x < -2 or x >= 6 | (-∞, -2) ∪ [6, ∞) | Two separate solution regions |
Formula Used
There is no arithmetic formula in this conversion. The calculator applies interval notation rules to each boundary value.
- Use ( ) when the boundary is not included. This matches < or >.
- Use [ ] when the boundary is included. This matches <=, >=, or =.
- Use ∪ when the solution has separate parts, such as x != a or x < a or x > b.
- Use -∞ or ∞ for unbounded sides. Infinity always uses parentheses.
How to Use This Calculator
- Type the inequality exactly as you see it in algebra class.
- Use one variable, such as x or y.
- Select your preferred decimal precision for endpoints.
- Click the convert button to generate interval notation.
- Review the interval, endpoint notes, and readable summary.
- Export the result as CSV or PDF when needed.
Convert Inequalities to Interval Notation
Converting an inequality to interval notation helps students read solution sets faster. It turns algebraic statements into a compact range. This format is common in algebra, precalculus, and calculus. It also makes graphing easier. When you see interval notation, you can quickly identify open endpoints, closed endpoints, and unbounded directions.
Why This Calculator Helps
This calculator accepts simple inequalities, compound inequalities, equalities, and not equal statements. It then converts them into interval notation with clear steps. You can enter forms such as x > 3, x <= 8, 2 < x < 7, or x != 5. The tool detects lower bounds, upper bounds, and unions. That saves time during homework, quizzes, and exam review.
How Interval Rules Work
Use parentheses for values not included in the solution. Use brackets for included values. For example, x > 4 becomes (4, ∞). The number 4 is excluded, so the left endpoint is open. Meanwhile, x >= 4 becomes [4, ∞). Here, 4 is included, so the bracket closes the endpoint. A double inequality like 1 <= x < 6 becomes [1, 6).
Compound and Union Cases
Compound inequalities often use and or or. The word and usually means intersection. The word or usually means union. For instance, x < -2 or x >= 5 becomes (-∞, -2) ∪ [5, ∞). A not equal statement also creates two intervals. So x != 3 becomes (-∞, 3) ∪ (3, ∞). These patterns appear often in algebra practice.
Study Smarter With Clear Output
Use this calculator to check classroom work, learn notation rules, and build confidence. The output shows interval notation, endpoint status, and a readable summary. Export tools also help you save results for notes. With repeated practice, converting inequalities becomes faster, cleaner, and more accurate across many math problems.
Many learners confuse brackets and parentheses. This tool reduces that error by labeling each endpoint as included or excluded. It also handles infinity correctly, because infinity never uses brackets. That detail matters in standardized tests. Accurate notation improves communication, supports graph interpretation, and strengthens understanding of real number solution sets.
It is useful for worksheets, tutoring sessions, digital lessons, and self-paced revision at home.
FAQs
1. What does interval notation represent?
Interval notation represents all real numbers that satisfy an inequality. It shows endpoints, inclusion, exclusion, and whether the solution continues toward negative or positive infinity.
2. When should I use parentheses?
Use parentheses when a boundary value is not included. Strict inequalities such as x > 2 or x < 9 always create open endpoints.
3. When should I use brackets?
Use brackets when the endpoint is included in the solution. Inclusive inequalities such as x >= 2, x <= 9, or x = 4 use closed endpoints.
4. Why does infinity always use parentheses?
Infinity is not a reachable endpoint. It describes endless direction, not a real number you can include. That is why interval notation always places infinity inside parentheses.
5. How are compound inequalities converted?
Compound inequalities combine two conditions. If both conditions hold together, the answer is one interval. If the conditions split apart, the answer becomes a union of intervals.
6. What happens with x != a?
A not equal statement excludes one value. The result becomes two open intervals, one on each side of that excluded number, joined by the union symbol.
7. Can this calculator read reverse inequalities?
Yes. It can interpret forms like 7 > x > 2 or 5 <= x. The tool flips the logic correctly before creating interval notation.
8. Can I save the result for later?
Yes. After conversion, you can export the result summary as a CSV file or generate a PDF copy for notes, assignments, or revision.