Automatically converts inequalities and interval notation in real-time.
This smart calculator instantly converts mathematical inequalities into interval notation — and interval notation back into inequalities — with fast, real-time results.
Easily switch between:
Just select the direction and enter your values — results update instantly.
Automatically handles open ( ) and closed [ ] intervals correctly.
The calculator displays:
Perfect for algebra students and exam preparation.
No manual calculation required. Results update automatically as you type, making it fast, accurate, and easy for homework, quizzes, and classroom learning.
Converting between inequalities and interval notation is essential in algebra. Interval notation provides a compact way to represent a set of numbers that satisfy an inequality. Understanding the rules and formulas behind these conversions helps students solve algebraic problems quickly and correctly.
1. One-Sided Inequalities:
x > a → (a, ∞), x ≥ a → [a, ∞), x < a → (-∞, a), x ≤ a → (-∞, a]
2. Two-Sided Inequalities:
a < x < b → (a, b), a ≤ x < b → [a, b), a < x ≤ b → (a, b], a ≤ x ≤ b → [a, b]
3. OR Compound Inequalities:
x < a OR x > b → (-∞, a) ∪ (b, ∞)
In these formulas:
Example 1: Convert the inequality x ≥ 3 to interval notation.
x ≥ 3 → [3, ∞)
Meaning: All real numbers greater than or equal to 3 satisfy the inequality.
Example 2: Convert the interval (-2, 5] back to inequality.
(-2, 5] → -2 < x ≤ 5
Meaning: All real numbers greater than -2 and less than or equal to 5 are included.
Step-by-Step Working:
This method ensures accurate conversion, which is crucial for graphing inequalities, solving algebraic problems, or preparing for exams. By learning these formulas, students can quickly write the interval notation of any inequality and understand its meaning in plain English.
The calculator automates these conversions, making it beginner-friendly while reinforcing the underlying formulas. It’s a practical tool for algebra homework, test preparation, and understanding real-number sets represented by inequalities and intervals.
If you enter:
x ≥ 3
The calculator converts it to:
[3, ∞)
This means all real numbers greater than or equal to 3.
Everything you need to know about converting inequalities and interval notation quickly and accurately.
It instantly converts inequalities (like x > 3 or 1 ≤ x < 5) into interval notation and vice versa, providing the result in math form and words.
Yes! It is completely free to use with no registration or hidden charges required.
Yes, the calculator supports one-sided inequalities (x > a), two-sided inequalities (a ≤ x < b), and OR compound inequalities (x < a OR x > b).
Absolutely! You can input an interval like (1, 5] and the calculator will generate the equivalent inequality form and a simple explanation in words.
Use the “Inequality Type” dropdown to choose one-sided, two-sided, or OR compound inequalities. The calculator will adjust the input fields automatically.
Yes, for each calculation the tool displays the inequality, interval notation, and a simple English explanation to help you understand the result.
Yes, the calculator is fully responsive and works smoothly on smartphones, tablets, laptops, and desktops.
Yes, use the “Clear All” button to reset inputs or the “Reload Calculator” button to reload the page completely.
Absolutely! This calculator is perfect for homework, quizzes, and exam practice. It provides instant, accurate results with clear explanations.
The calculator correctly handles open ( ) and closed [ ] intervals, infinite intervals (like (-∞, a) or [b, ∞)), and compound intervals.
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