Graph inequalities on number lines

An inequality shows that two values are not equal. Graphing them on a number line is a great way to see all the possible numbers that can be a solution. It's a visual map of all the right answers!

Do this: Read the concept below, then try the quiz or activity.

Lesson 150 of 215

Concept

An inequality compares two values, showing if one is less than (<), greater than (>), less than or equal to (≤), or greater than or equal to (≥). Graphing them helps visualize all the possible solutions.

The Two Types of Circles

1.  Open Circle (○):
    *   Used for "less than" (<) and "greater than" (>).
    *   It means the number itself is not included in the solution.
2.  Closed Circle (●):
    *   Used for "less than or equal to" (≤) and "greater than or equal to" (≥).
    *   It means the number itself is included in the solution.

Graphing the Four Basic Inequalities

1.  x > 3: "x is greater than 3"
    *   Draw an open circle on 3 (because 3 is not greater than 3).
    *   Draw an arrow to the right, because all numbers to the right (4, 5, 6...) are greater than 3.
    <--|---|---|---⚪----&gt;
           1   2   3   4

2.  x < 3: "x is less than 3"
    *   Draw an open circle on 3.
    *   Draw an arrow to the left, because all numbers to the left (2, 1, 0...) are less than 3.
    <----⚪---|---|---|---&gt;
           2   3   4   5

3.  x ≥ 3: "x is greater than or equal to 3"
    *   Draw a closed circle on 3 (because 3 is equal to 3).
    *   Draw an arrow to the right.
    <--|---|---|---⚫----&gt;
           1   2   3   4

4.  x ≤ 3: "x is less than or equal to 3"
    *   Draw a closed circle on 3.
    *   Draw an arrow to the left.
    <----⚫---|---|---|---&gt;
           2   3   4   5

Key Idea: The inequality symbol points in the same direction that your arrow should go on the number line!

Try it

Practice: Graph inequalities on number lines.

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