# Graphing Inequalities on a Number Line Calculator

URL: https://speedycalculator.com/calculators/math/graphing-inequalities-1d/
Last updated: 2026-10-30

> The number line inequality calculator combines up to three inequalities such as x ≥ −1 and x < 3, writes the solution in interval notation and draws it on a text number line (● included, ○ excluded).

## Inputs

- Number of inequalities
- Combine with
- Inequality 1: x is
- Value 1
- Inequality 2: x is
- Value 2
- Inequality 3: x is
- Value 3

## Results

- Solution (interval notation)
- Inequalities
- Number line

## Formula

```
x < a → (−∞, a)   x ≤ a → (−∞, a]   x > a → (a, ∞)   x ≥ a → [a, ∞)
```

## Explanation

Graphing inequalities on a number line is the first step to understanding solution sets. A filled circle means the endpoint is included, an open circle means it is not, and the shaded part shows every number that satisfies the condition.

### How to use the Graphing Inequalities on a Number Line Calculator

- **Number of inequalities**
- **Combine with**
- **Inequality 1: x is**
- **Value 1**
- **Inequality 2: x is**
- **Value 2**
- **Inequality 3: x is**
- **Value 3**

Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.

### How it works

With "and" the calculator intersects the conditions (all must be true); with "or" it takes their union (at least one is true). The bold segment of the number line shows the solution.

## Worked example

Inputs — Number of inequalities: 2; Combine with: and (all must hold); Inequality 1: x is: ≥ (greater than or equal to); Value 1: -1; Inequality 2: x is: < (less than); Value 2: 3.

Results — **Solution (interval notation) = [−1, 3)**; Inequalities = x ≥ −1 and x < 3; Number line = ──────────●━━━━━━━━━━━━━━━━━━━○──────────
−3 5.

## Key terms

- **Number line**: A line on which every point represents a real number.

## FAQ

**What does a closed dot mean?**
The endpoint is included (≤ or ≥).

**What does an open dot mean?**
The endpoint is excluded (< or >).

**What is the difference between "and" and "or"?**
"And" keeps only the overlap; "or" keeps everything covered by at least one inequality.

**Can a compound inequality have no solution?**
Yes, for example x < 1 and x > 3.


## Sources

- [OpenStax – College Algebra 2e](https://openstax.org/details/books/college-algebra-2e)
- [OpenStax – Intermediate Algebra 2e](https://openstax.org/details/books/intermediate-algebra-2e)