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Concept

# Graphing an Inequality on a Number Line

The graph of a one-variable inequality is a visual representation of the inequality's solution set, which can be drawn on a number line in three steps:

1. Identify if the inequality is strict.
2. Draw the boundary point;
• use an open point $(\circ)$ for strict or
• use a closed point $(\bullet)$ for non-strict.
3. Shade the rest of the solution set.

An arrow in either direction indicates that all numbers in that direction are part of the solution set.

$x \ge 0$

$x \leq 2$

$x > \text{-} 3$

The inequality $x \geq 0$ is graphed with a closed circle at $x = 0$ and an arrow pointing to the right. Since $0$ solves the inequality, the circle is closed. Additionally, the direction of the arrow points toward numbers greater than $0$, since the inequality symbol is $\geq.$