Turn inequality expressions into interval notation quickly. Review endpoints, unions, and bounded sets. Get clean results with practical examples today.
| Inequality | Interval Notation | Meaning |
|---|---|---|
| x > 5 | (5, ∞) | Greater than 5 |
| x <= 3 | (-∞, 3] | Less than or equal to 3 |
| 2 < x <= 7 | (2, 7] | Between 2 and 7 |
| x != 4 | (-∞, 4) ∪ (4, ∞) | All reals except 4 |
| x < 1 or x >= 4 | (-∞, 1) ∪ [4, ∞) | Two separate ranges |
Interval notation records every value that satisfies an inequality. Parentheses show excluded endpoints. Brackets show included endpoints. Infinity always uses parentheses.
Use these rules:
Compound inequalities joined by and form one bounded interval. Compound inequalities joined by or usually form a union of intervals.
Interval notation gives a compact way to write solution sets. It is used in algebra, graphing, calculus, and exam work. A clear interval statement helps students check endpoints fast. It also shows whether boundary values are included or excluded.
Parentheses mean the endpoint is not included. Brackets mean the endpoint is included. This small difference changes the final answer. For example, x > 4 becomes (4, ∞). But x >= 4 becomes [4, ∞). That one symbol matters.
Simple inequalities are the easiest to convert. If the variable is greater than a number, write the number first and extend right to infinity. If the variable is less than a number, write negative infinity first and end at that number. Always keep infinity with parentheses.
Compound inequalities often use the words and or or. The word and usually means a shared region. That produces one interval. The word or usually means separate solution parts. That produces a union of intervals. This calculator reads both common structures and shows the matching interval notation.
A double inequality places the variable between two values. Examples include 2 < x <= 7 or -3 <= x < 5. The left symbol controls the left endpoint. The right symbol controls the right endpoint. This tool converts both sides at once.
Many learners mix up brackets and parentheses. Others place infinity inside brackets. That is incorrect. Infinity is never an endpoint you can include. Another common mistake is forgetting unions when solving not equal inequalities. This calculator helps reduce those errors and gives clean output.
It shows all numbers that satisfy an inequality in a compact range format. It also shows whether the boundary values are included or excluded.
Use parentheses when an endpoint is not included. They are also always used with positive infinity and negative infinity.
Use brackets when the endpoint is included in the solution. This happens with less than or equal to, and greater than or equal to signs.
It becomes two intervals: (-∞, 5) ∪ (5, ∞). The value 5 is excluded, so both endpoints at 5 stay open.
The union symbol combines separate solution intervals. It is used when an inequality has two valid regions, usually from an or statement.
Yes. It handles common and statements, or statements, and double inequalities with mixed open and closed endpoints.
Infinity is not a fixed number or reachable endpoint. Because of that, interval notation always uses parentheses with infinity.
Yes. The result includes a number line guide. It tells you where to place open or closed points and which side to shade.