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Graphing an Inequality on a Number Line

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.

x0x \ge 0

x2x \leq 2

x>-3x > \text{-} 3

The inequality x0x \geq 0 is graphed with a closed circle at x=0x = 0 and an arrow pointing to the right. Since 00 solves the inequality, the circle is closed. Additionally, the direction of the arrow points toward numbers greater than 00, since the inequality symbol is .\geq.

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