Represent inequalities on a number line

A one-variable inequality is represented on a number line by showing its entire solution set: an open endpoint for a value not included ( $<$ or $>$ ) and a closed endpoint for a value included ( $\le$ or $\ge$ ), with shading toward all values that satisfy the relationship. The representation applies to rational-number solutions, including positive and negative fractions and decimals, and emphasizes that an inequality describes a range rather than a single value; systems of inequalities and formal interval notation are not included.

Detailed Explanation: 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 $x>-1.5$ .

Learn by doing: Represent inequalities on a number line

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Inequalities - Single - Inequality to Number Line

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