How to Graph Inequalities on a Number Line

Graphing inequalities on a number line is an important skill in math, especially in Year 7 Algebra. When you learn to show inequalities visually, it helps you understand math statements better.

Types of Inequalities

1. Open Inequalities: These do not include the endpoint in their solution.

   • Examples:
     • (x < 5)
     • (y > -2)

2. Closed Inequalities: These do include the endpoint.

   • Examples:
     • (x \leq 3)
     • (y \geq 0)

Steps to Graph Inequalities

1. Identify the inequality:

   • First, find out if the inequality is open or closed. This will tell you what kind of circle to use in the graph.

2. Draw the number line:

   • Make a straight horizontal line and add evenly spaced numbers on it.

3. Plot the endpoint:

   • For open inequalities (like (x < 5)), draw an open circle at the endpoint (5) to show that 5 is not included.
   • For closed inequalities (like (x \leq 3)), draw a closed circle at the endpoint (3) to show that 3 is included.

4. Shade the right area:

   • For (x < 5), shade to the left of 5 to show that all values less than 5 work with the inequality.
   • For (x \geq 3), shade to the right of 3 to show that all values greater than or equal to 3 work with the inequality.

Example

• For the inequality (x < 4):

  • Draw an open circle at 4 and shade to the left.

• For the inequality (x \geq 2):

  • Draw a closed circle at 2 and shade to the right.

Conclusion

Graphing inequalities on a number line gives us important information about how numbers relate to each other. By learning this skill, students can improve their understanding of math and be ready for more complicated topics later on.