Teaching Graphing Inequalities on a Number Line

Instructor: Brittany Rasmussen

Brittany has a bachelor's degree in elementary education and a master's in special education. She has taught at the elementary, middle school and high school levels.

This lesson will cover methods for teaching students how to graph inequalities on a number line. It will offer basic instructions as well as ideas for assessment and differentiation to reach all learners.

Solving an Inequality

In order for students to be successful with this lesson, they must already know how to solve an equation. If your student(s) don't know how to do that, go back and teach that skill before beginning this lesson.

The first step in graphing an inequality is solving the inequality. Remind students that solving an inequality is much like solving an equation - they should get the variable by itself on one side. It is important to note that there is one big difference between solving an inequality and solving an equation: when you multiply or divide both sides by a negative number, you have to change the direction of the sign. So, for example, a 'greater than or equal to' would become a 'less than or equal to' after you multiply OR divide by a negative number.

Graphing a Solved Inequality

Once the inequality is solved, you should have a solution that looks something like this: x > 7. This means that x is all the numbers that are greater than 7. On a number line, students should draw a line to the right of 7, since all those numbers are included. They should draw a circle around the point for seven since seven isn't included. Be sure your students use an arrow at the end of the number line to show that the solution includes all the numbers greater than 7, even the ones that won't fit on the number line. You might want to emphasize that the line really goes on forever, but obviously, our papers aren't large enough to hold forever, so we use an arrow to show that forever is included but won't fit.

If the solution includes an equal sign, such as ≤ or ≥, you will need to make sure the circle on the number line is filled in to show that the number is included. The solution is greater than or equal to, meaning that the number is included in the solution.

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