**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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