Understanding Inequality Conversion
Inequality notation describes where a variable can live. Interval notation writes the same solution as a range. This calculator helps convert common inequality forms into clean interval notation. It handles strict signs, inclusive signs, compound statements, unions, intersections, equations, and not equal cases.
Why Interval Notation Matters
Interval notation is compact. It shows open endpoints with parentheses. It shows included endpoints with square brackets. Infinity always uses parentheses. This style is useful in algebra, calculus, statistics, domains, ranges, and graphing. A short interval can replace a long inequality sentence. It also makes unions easier to read.
What This Calculator Checks
The tool reads a direct inequality, such as x >= 4. It also reads a bounded form, such as -2 < x <= 7. You can enter compound statements with and or or. The solver also accepts simple linear inequalities, such as 2x + 3 <= 11. When the coefficient is negative, the relation sign is reversed during solving. This is important because division by a negative number changes the inequality direction.
Open And Closed Endpoints
A strict inequality uses an open endpoint. For example, x < 5 becomes (-∞, 5). The number 5 is not included. An inclusive inequality uses a closed endpoint. For example, x <= 5 becomes (-∞, 5]. The number 5 is included. A double inequality combines two endpoint decisions in one interval.
Compound Results
The word and means overlap. The answer is the intersection of both conditions. For example, x > 2 and x < 8 becomes (2, 8). The word or means either condition may work. The answer is usually a union. For example, x < 1 or x >= 4 becomes (-∞, 1) ∪ [4, ∞).
Practical Use
Use the calculator to verify homework, prepare examples, or check domain restrictions. Enter the inequality exactly as written. Then review the interval, endpoint notes, and export options. The CSV file is helpful for records. The PDF file is useful for worksheets and quick sharing.
Accuracy Tips
Use a clear variable name. Leave spaces around and or or. Use <= for less than or equal. Use >= for greater than or equal. Avoid mixing many variables in one line. For manual entries, choose each endpoint carefully. Mark included endpoints only when the original inequality allows equality. Check final notation before exporting.