Graphing Inequalities on a Real Number Line in 2026
Graphing linear inequalities on a one-dimensional coordinate number line communicates solution sets visually:
- Open Circle (○): Used for strict inequalities ($<$ and $>$). The boundary point itself is excluded.
- Closed Solid Circle (●): Used for inclusive inequalities ($\le$ and $\ge$). The boundary point itself is included.
- Arrow Shading: Indicates all real numbers in that direction satisfy the inequality.
Number Line Conventions Reference Table
| Inequality | Circle Type | Shading Direction | Interval Notation |
|---|---|---|---|
| $x < a$ | Open Circle (○) | Left ($leftarrow$) | $(-\infty, a)$ |
| $x \le a$ | Closed Circle (●) | Left ($leftarrow$) | $(-\infty, a]$ |
| $x > a$ | Open Circle (○) | Right ($\rightarrow$) | $(a, \infty)$ |
| $x \ge a$ | Closed Circle (●) | Right ($\rightarrow$) | $[a, \infty)$ |