**The graphing iInequalities number line calculator processes mathematical expressions containing inequality symbols (<, >, ≤, ≥, ≠) and translates them into clear visual representations. **

When solving “x > 3”, the calculator would draw a number line with an **open circle** at 3 and an **arrow extending to the right**, indicating all numbers greater than 3.

Let’s solve x ≥ -2:

**-5 -4 -3 -2 -1 0 1 2 3 4 5
●--------------------→**

The **solid dot** at -2 and the **arrow extending right** shows all numbers greater than or equal to -2.

## Graphing Inequalities on a Number Line Calculator

Inequality | Solution Type | Boundary Points | Circle Type | Direction |
---|---|---|---|---|

x > 2 | Simple | 2 | Open | Right |

x ≤ -1 | Simple | -1 | Closed | Left |

-3 < x ≤ 4 | Compound | -3, 4 | Open, Closed | Between |

x < 0 or x ≥ 5 | Multiple | 0, 5 | Open, Closed | Split |

x ≥ 1 and x < 3 | Compound | 1, 3 | Closed, Open | Between |

-5 < x < -2 | Compound | -5, -2 | Open, Open | Between |

x ≠ 4 | Simple | 4 | Open | All directions except right |

x ≤ 0 or x > 2 | Multiple | 0, 2 | Closed, Open | Split |

-1 < x ≤ 2 | Compound | -1, 2 | Open, Closed | Between |

x < -3 or x ≥ 1 | Multiple | -3, 1 | Open, Closed | Split |

x > -2 and x ≤ 5 | Compound | -2, 5 | Open, Closed | Between |

x = 0 | Simple | 0 | Closed | None |

## Graphing Inequalities on a Number Line Formula

Here are the key formulas and rules:

- For strict inequalities (< or >):
- Use an
**open circle**(○) at the boundary point - Draw an
**arrow in the appropriate direction**

- Use an
- For inclusive inequalities (≤ or ≥):
- Use a
**closed circle**(●) at the boundary point - Draw an
**arrow in the appropriate direction**

- Use a

For the inequality -3 < x ≤ 4:

**-5 -4 -3 -2 -1 0 1 2 3 4 5
○------------------●**

**x ≥ 1 and x < 3**: This represents all numbers from **1** (inclusive) to **3** (exclusive).

text`-5 -4 -3 -2 -1 0 1 2 3 4 5`

●-----------○

## How do I graph an inequality on a number line?

**Step 1: Identify Your Number Line Point**

- For
**“less than”**(<) or**“greater than”**(>): Use an**open circle**○ - For
**“less than or equal to”**(≤) or**“greater than or equal to”**(≥): Use a**closed/filled circle**●

**Step 2: Draw Your Direction**

- For
**“less than”**or**“less than or equal to”**: Draw an**arrow going left** - For
**“greater than”**or**“greater than or equal to”**: Draw an**arrow going right**

**Let’s graph x < 5:**

- Boundary point is 5
- Solution includes all numbers less than 5
- Use an
open circleat 5 since < excludes 5- Arrow points left from 5
`-5 -4 -3 -2 -1 0 1 2 3 4 5 ←--------------------○`

## Example of Graphing Inequalities

Let’s explore some **practical examples**:

**Compound Inequality**: -2 ≤ x < 3 `-5 -4 -3 -2 -1 0 1 2 3 4 5 ●-----------○`

**Multiple Inequalities**: x < -1 or x ≥ 4 `-5 -4 -3 -2 -1 0 1 2 3 4 5 ←--------------○ ●--------→`

## What is Graphing Inequalities on a Number Line?

Graphing inequalities on a number line is a **fundamental mathematical skill** that involves representing mathematical relationships where variables can take on multiple values.

The method uses standardized notation to show:

**Included values**(solid dots)**Excluded values**(open circles)**Continuous ranges**(lines with arrows)**Direction of solutions**(left or right arrows) References:

`Purplemath - "Graphing Inequalities" - https://www.purplemath.com/modules/ineqgrph.htm`

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