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