Master inequality notation without confusion today. See open and closed endpoints with exact interval formatting. Check steps, download results, and learn faster with examples.
| Input | Solved Form | Interval Notation | Endpoint Meaning |
|---|---|---|---|
| 2x + 4 < 10 | x < 3 | (-∞, 3) | 3 is open |
| 5x - 15 ≥ 0 | x ≥ 3 | [3, ∞) | 3 is closed |
| 2 < 3x + 1 ≤ 13 | 1/3 < x ≤ 4 | (0.333333, 4] | Left open, right closed |
| -2x + 6 > 0 | x < 3 | (-∞, 3) | Sign reverses after division |
Single inequality: ax + b ? c
Subtract b from both sides. Then divide by a.
x ? (c - b) / a
If a is negative, reverse the inequality sign after division.
Compound inequality: L <= ax + b <= U or L < ax + b < U
Subtract b from all three parts. Then divide every part by a.
For positive a, the order stays the same. For negative a, both inequality signs reverse.
Use parentheses for open endpoints. Use brackets for closed endpoints.
A linear inequality interval notation calculator helps you solve faster. It turns algebra steps into clear interval answers. This matters in classwork, homework, and test review. You can check a single inequality or a compound inequality. You can also confirm endpoint rules with less guesswork.
Linear inequalities compare values with symbols like less than or greater than. The goal is to find every value of x that makes the statement true. After solving, the answer is written in interval notation. This format shows ranges, endpoints, and whether boundary values are included.
Interval notation is compact and easy to read. Parentheses show open endpoints. Brackets show closed endpoints. For example, x > 3 becomes (3, ∞). The value 3 is not included. If x ≥ 3, the interval becomes [3, ∞). The endpoint changes because 3 is included.
Compound inequalities also become easier to interpret. A statement like 2 < x ≤ 7 becomes (2, 7]. That answer tells you the lower endpoint is open. It also shows the upper endpoint is closed. This is useful in algebra, precalculus, and data range analysis.
This calculator solves expressions in the form ax + b ? c. It also solves compound forms like L < ax + b ≤ U. It isolates x, handles negative coefficients, and reverses inequality signs when needed. Then it converts the final answer into interval notation and set builder notation.
You also get simplified steps. That helps you learn the solving process, not only the final answer. The calculator highlights whether the result is open, closed, bounded, unbounded, empty, or all real numbers. It also supports quick CSV export and PDF download for study notes.
Use this tool when checking practice problems, verifying homework, or building revision sheets. It is also useful for teachers who need fast examples. Because the layout is simple, the page stays readable on desktop, tablet, and mobile screens. That makes repeated algebra practice easier.
Careful interval notation reduces common mistakes. Students often confuse parentheses and brackets. This page separates those cases clearly and shows when equality changes the endpoint style. It also reminds learners that negative division changes the comparison sign.
Interval notation is a compact way to show all solution values on a number line. Parentheses mean the endpoint is excluded. Brackets mean the endpoint is included.
The sign reverses only when you divide or multiply both sides by a negative number. This rule keeps the statement mathematically true.
An open endpoint means the boundary value is not part of the solution. A closed endpoint means the boundary value is included in the solution set.
Yes. It solves compound inequalities with a lower bound and an upper bound. It then converts the result into interval notation and set builder notation.
The variable term disappears. The inequality becomes a constant statement. That means the answer is either all real numbers or no solution.
Infinity symbols show the solution continues forever in one direction. They are always written with parentheses because infinity is not a reachable endpoint.
Yes. The calculator accepts decimal entries for coefficients, constants, and bounds. Results are shown in a clean rounded format for readability.
You can save the current result for revision, sharing, or printing. CSV is useful for records. PDF is useful for quick study sheets.
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.