Skill: Represent inequalities on a number line

An inequality represents a range of values, not just one answer.

• Use an open circle for a value that is not included: $<$ or $>$.
• Use a closed circle for a value that is included: $\le$ or $\ge$.
• Shade toward the numbers that make the inequality true:
  • Shade right for “greater than.”
  • Shade left for “less than.”

Example

Represent the inequality

$$x>-1.5$$

Step 1: Find the boundary value.
The boundary value is $-1.5$. This is where the shading will begin.

Step 2: Choose the endpoint.
The symbol is $>$, not $\ge$, so $-1.5$ is not included. Draw an open circle at $-1.5$.

Step 3: Choose the shading direction.
The inequality says $x$ is greater than $-1.5$. Greater numbers are to the right, so shade to the right.

$$\text{←──────○════════════════→}$$

The open circle is at $-1.5$. The shaded part includes numbers such as $-1$, $0$, and $2$, but not $-1.5$ itself. Thus, the number line shows every solution to $x>-1.5$.