This inequality to interval notation calculator accepts an inequality in the form of “x > 3”, “x ≤ 5”, or a compound form such as “-2 < x ≤ 5” and returns the equivalent interval notation.
Input: -3 ≤ x < 4
Calculator Processing:
- Identifies lower bound: -3 (inclusive)
- Identifies upper bound: 4 (exclusive)
Output: [-3,4)Inequality to Interval Notation Calculator
| Inequality Expression | Interval Notation |
|---|---|
| -3 ≤ x ≤ 7 | [-3,7] |
| 2 < x < 9 | (2,9) |
| x ≥ 4 | [4,∞) |
| x < -1 | (-∞,-1) |
| 0 ≤ x < 5 | [0,5) |
| -5 < x ≤ 0 | (-5,0] |
| x > 10 | (10,∞) |
| -2 ≤ x < 3 | [-2,3) |
| 1 < x ≤ 4 | (1,4] |
| x = -3 | [-3,-3] |
| -∞ < x < ∞ | (-∞,∞) |
| x ≤ -1 or x > 2 | (-∞,-1] ∪ (2,∞) |
| 3 < x < 7 and x ≥ 5 | (5,7) |
| -4 ≤ x < -2 | [-4,-2) |
| x = 0 or x = 1 | [0,0] ∪ [1,1] |
| -6 < x ≤ -3 or x > 1 | (-6,-3] ∪ (1,∞) |
Inequality to Interval Notation Formula
For Single Inequalities:
- x > a becomes (a, ∞)
- x ≥ a becomes [a, ∞)
- x < b becomes (-∞, b)
- x ≤ b becomes (-∞, b]
- For ≤ (less than or equal to): Use [ bracket
- For < (less than): Use ( parenthesis
- For ≥ (greater than or equal to): Use ] bracket
- For > (greater than): Use ) parenthesis
Inequality: 2 ≤ x ≤ 7
Formula Application:
- Left bound (2): Use [ because of ≤
- Right bound (7): Use ] because of ≤
Interval Notation: [2,7]How to Convert Inequality to Interval Notation?
Converting inequalities to interval notation requires following a approach:
- Identify the bounds of the inequality.
- Determine inclusivity based on inequality symbols.
- Choose appropriate brackets or parentheses.
- Write the interval from left to right.
Given: -1 < x ≤ 6
Step 1: Bounds are -1 and 6.
Step 2: -1 is exclusive, 6 is inclusive.
Step 3: Use ( for -1, ] for 6.
Step 4: Write as (-1,6].What is the Interval Notation of a Line?
The interval notation of a line represents its continuous extent in one-dimensional space. It can be:
- Bounded: Has both endpoints, like [2, 8]
- Semi-bounded: Has one infinite end, like (-∞, 5]
- Unbounded: Extends infinitely, like (-∞, ∞)
Line segment from 3 to 8: [3,8]
Ray from 5 to infinity: [5,∞)
Entire real line: (-∞,∞)What is the Symbol for Interval Notation Inequality?
Interval notation uses specific symbols to represent different types of ranges:
- [ ]: Closed interval (inclusive).
- ( ): Open interval (exclusive).
- ∞: Infinity.
- -∞: Negative infinity.
- ,: Separator between endpoints.
x ≥ 4: [4,∞)
-2 < x < 3: (-2,3)
x = 5: [5,5]Sources and References
- Mathematics LibreTexts – “Interval Notation” https://math.libretexts.org/Bookshelves/Precalculus/Book%3A_Precalculus_(OpenStax)/01%3A_Functions/1.2%3A_Domain_and_Range
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