Build interval notation from simple or compound inequalities. See open and closed endpoints with confidence. Download neat results, tables, and guides for daily study.
Use the left bound for greater than, equal, and not equal forms. Use the right bound for less than forms. Use both bounds for between and outside forms.
| Inequality | Interval Notation | Endpoint Rule | Graph Note |
|---|---|---|---|
| x > 4 | (4, ∞) | Open at 4 | Shade right |
| x ≥ -2 | [-2, ∞) | Closed at -2 | Shade right |
| x < 7 | (-∞, 7) | Open at 7 | Shade left |
| -3 < x ≤ 5 | (-3, 5] | Open at -3, closed at 5 | Shade between bounds |
| x ≤ -4 or x > 6 | (-∞, -4] ∪ (6, ∞) | Closed at -4, open at 6 | Shade outside gap |
| x ≠ 1 | (-∞, 1) ∪ (1, ∞) | Open at 1 | Shade both sides |
This calculator converts inequality symbols into interval notation, set builder notation, and number line rules.
| Form | Interval Rule |
|---|---|
| x > a | (a, ∞) |
| x ≥ a | [a, ∞) |
| x < b | (-∞, b) |
| x ≤ b | (-∞, b] |
| a < x < b | (a, b) |
| a ≤ x ≤ b | [a, b] |
| x = a | [a, a] |
| x ≠ a | (-∞, a) ∪ (a, ∞) |
Parentheses mean an open endpoint. Brackets mean a closed endpoint. A union symbol joins two separate solution parts.
Step 1: Enter the variable name. Most users keep x.
Step 2: Choose the solution type that matches your inequality.
Step 3: Enter the needed bound values.
Step 4: Tick endpoint boxes when the value is included.
Step 5: Click Calculate.
Step 6: Read the inequality form, interval notation, set builder form, and graph note.
Step 7: Use the CSV or PDF button to save the result.
This graphing inequalities interval notation calculator helps you move between symbols, interval notation, and a number line view. Many students can solve an inequality but still struggle to write the answer correctly. This tool fixes that gap. You can enter a one sided inequality, a compound inequality, an exact value, or a not equal form. The result section shows the inequality form, interval notation, set builder notation, endpoint rules, and a simple graph note. It also explains whether the solution is a finite interval, a ray, a union, or a single point.
Interval notation is compact and precise. It helps you describe a full solution set without writing many words. In algebra, precalculus, and calculus, teachers often expect answers in interval form. Standardized tests also use this style. Parentheses tell you that an endpoint is not included. Brackets tell you that an endpoint is included. Infinity always uses parentheses because infinity is not a reachable number. Once you understand this pattern, you can translate inequalities faster. That saves time during homework, quizzes, and review sessions.
Open and closed endpoints are the heart of graphing inequalities. A greater than sign creates an open point unless the symbol includes equality. A less than sign works the same way on the other side. For compound inequalities, the middle section becomes the interval. For outside inequalities, the two outer rays form a union. Equal to gives one exact point. Not equal to removes one point and keeps the rest of the number line. These rules may look small, but they change the answer completely. One wrong bracket can make the final solution incorrect.
Use this calculator to check classwork, build examples, and review graphing steps before a test. It is useful for solving linear inequalities, absolute value cases after splitting, and domain restrictions in advanced topics. The example table gives quick patterns you can memorize. The formula section shows the main conversion rules. The export options help you save practice results for later study. With repeated use, you will spot interval notation patterns quickly, write cleaner answers, and graph inequalities with more confidence and fewer mistakes.
Interval notation is a short way to show solution sets on the number line. It uses parentheses for open endpoints and brackets for closed endpoints.
Use parentheses when the endpoint is not included. This happens with strict inequalities such as greater than or less than. Infinity also always uses parentheses.
Use brackets when the endpoint is included in the solution. This happens with symbols that include equality, such as greater than or equal to and less than or equal to.
Infinity is not a fixed number that can be reached or included. It only shows direction. That is why interval notation always uses parentheses with infinity.
The union symbol joins two separate solution parts. It is common in outside inequalities and not equal expressions where the graph splits into two regions.
Yes. Choose between two bounds for middle intervals or outside two bounds for split solutions. Then enter both endpoints and select inclusion rules.
Graphing shows the solution visually on a number line. Interval notation writes the same solution in a compact symbolic form. Both should match exactly.
Yes. It helps you verify brackets, endpoint inclusion, unions, and graph direction. That makes it useful for algebra homework, quizzes, and exam review.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.