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!
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. <--|---|---|---⚪----> 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. <----⚪---|---|---|---> 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**. <--|---|---|---⚫----> 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**. <----⚫---|---|---|---> 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.