Convert inequalities and interval notation instantly.
This calculator helps you convert inequalities into interval notation and interval notation back into inequalities instantly. It's perfect for algebra homework, exam practice, and understanding sets of numbers.
Simply enter an inequality:
x > 3
And the calculator outputs:
(3, ∞)
Enter an interval like:
[2, 5)
The calculator converts it into:
2 ≤ x < 5
Supports AND / OR inequalities:
The calculator also shows inequalities in words for easier understanding:
x ≥ 3 → x is greater than or equal to 3
1️⃣ Choose the mode: Inequality → Interval or Interval → Inequality.
2️⃣ For inequalities:
3️⃣ For intervals:
4️⃣ Edge cases handled:
Interval notation is a concise way to describe a set of numbers on the number line. It uses brackets [ ] and parentheses ( ) to indicate whether endpoints are included or excluded. Understanding the formulas for converting between inequalities and interval notation helps in algebra, calculus, and problem-solving.
One-Sided Inequalities → Interval Notation
x > a → (a, ∞)
x ≥ a → [a, ∞)
x < a → (-∞, a)
x ≤ a → (-∞, a]
Two-Sided Inequalities → Interval Notation
a < x < b → (a, b)
a ≤ x < b → [a, b)
a < x ≤ b → (a, b]
a ≤ x ≤ b → [a, b]
Compound Inequalities → Interval Notation
x > a AND x < b → (a, b)
x ≥ a AND x ≤ b → [a, b]
x < a OR x > b → (-∞, a) ∪ (b, ∞)
x ≤ a OR x ≥ b → (-∞, a] ∪ [b, ∞)
Key Points:
For example, if we have a compound inequality like x ≥ 2 AND x < 6, the corresponding interval notation formula is:
[2, 6)
This formula section helps students quickly reference how inequalities are translated into intervals, which is especially useful for algebra homework, exams, or online practice problems. By understanding these formulas, you can easily convert back and forth between inequalities and interval notation without confusion.
1️⃣ Enter the inequality:
x ≥ 2 AND x < 6
The calculator converts it into interval notation:
[2, 6)
2️⃣ Enter interval notation:
(-∞, 3) ∪ (5, ∞)
The calculator converts it into inequality:
x < 3 OR x > 5
Everything you need to know about converting inequalities to interval notation and vice versa.
It converts inequalities (one-sided, two-sided, or compound) into interval notation and converts interval notation back into inequalities in words or symbolic form instantly.
It supports one-sided inequalities (e.g., x > 3), two-sided inequalities (e.g., 2 ≤ x < 5), and compound inequalities using AND / OR statements (e.g., x < 1 OR x > 4).
Yes. You can enter intervals with positive or negative infinity, such as (-∞, 5] or [3, ∞), and the calculator converts them correctly into inequalities.
The calculator parses AND and OR conditions separately. For AND, it returns a single interval; for OR, it returns a union of intervals (∪) accurately representing all valid values of x.
Yes. Single-value intervals like [5, 5] are converted to x = 5. Intervals that contain no numbers are shown as the empty set (∅).
For one-sided inequalities, only the lower (or upper) bound is required. For two-sided or compound inequalities, both bounds must be entered for accurate conversion.
Absolutely. The calculator is fully responsive and works smoothly on smartphones, tablets, laptops, and desktop computers.
Yes. It is completely free and works instantly without registration, downloads, or hidden costs.
If bounds are invalid (e.g., lower bound > upper bound for two-sided inequalities), the calculator shows an error message indicating that a must be less than b.
The calculator accurately converts between inequalities and interval notation for all supported types, including one-sided, two-sided, and compound inequalities with unions and infinities.
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