Graph inequalities on a number line

An inequality such as $x>-2$ or $x\le3$ describes a set of possible values rather than one value; its number-line graph shows that solution set with an open endpoint for a strict comparison, a closed endpoint for an inclusive comparison, and shading toward values that satisfy the inequality. The focus is on integers and familiar rational numbers, including interpreting boundary points and checking solutions, not compound inequalities or formal interval notation.

Detailed Explanation: Graph inequalities on a number line

An inequality describes many possible values. To graph it on a number line:

Find the boundary number.
Use an open circle if the inequality is $<$ or $>$ . The boundary is not included.
Use a closed circle if the inequality is $\le$ or $\ge$ . The boundary is included.
Shade in the direction of the values that make the inequality true.

Example: Graph $(x \le 3)$

Step 1: Find the boundary number.

The boundary number is $3$ .

Step 2: Choose the endpoint.

The symbol is $\le$ , which means “less than or equal to.” Since $x$ is allowed to equal $3$ , use a closed circle at $3$ .

Step 3: Choose the shading direction.

Numbers less than $3$ are to the left of $3$ , so shade to the left.

<==========●---------------->
           3

The graph represents all numbers that are less than or equal to $3$ , such as $3$ , $2$ , $0$ , and $(-4)$ .

To check, try a shaded value and an unshaded value:

$(2 \le 3)$ is true, so $2$ belongs in the shaded part.
$(5 \le 3)$ is false, so $5$ does not belong in the shaded part.

Learn by doing: Graph inequalities on a number line

Click a topic below to practice the foundational skills you'll need, learn the steps, or master this skill

Practice with unlimited practice problems

Function Domain/Range Definition - Set Builder to Number Line (Without Union)

Earned ?