Learn to read and write inequalities and graph them on a number line.

1. Learn to read and write inequalities and graph them on a number line.

2. Vocabulary inequality algebraic inequality solution set compound inequality

3. An inequality states that two quantities either are not equal or may not be equal. An inequality uses one of the following symbols:

4. An inequality that contains a variable is an algebraic inequality . A value of the variable that makes the inequality true is a solution of the inequality. An inequality may have more than one solution. Together, all of the solutions are called the solution set. A compound inequality is the result of combining two inequalities. The words and and or are used to describe how the two parts are related.

5. Additional Example 1: Writing Inequalities Write an inequality for each situation. A. There are at least 15 people in the waiting room. number of people ≥ 15 B. The tram attendant will allow no more than 60 people on the tram. number of people ≤ 60

6. Check It Out Example 1 A. There should be no more than 10 people on an elevator number of people ≤ 10 B. There must be at least 20 people signed up for a class or it will be canceled. number of people ≥ 20

7. Additional Example 2: Graphing Simple Inequalities Graph each inequality. • n<3. • a>=24

8. Check It Out Example 2 Graph each inequality. • n<-1 • j<=0

9. Additional Example 3A : Graphing Compound Inequalities Graph each compound inequality. • m ≤ –2 or m > 1 Graph m ≤ –2. Graph m > 1.

10. Continued: Example 3A Graph the common solutions.

11. Additional Example 3B : Graphing Compound Inequalities • -3 < b ≤ 0 Graph -3 < b. Graph b ≤ 0

12. Continued: Example 3B Graph the common solutions.

13. Check It Out Example 3 Graph each compound inequality. Graph x > 4 Graph x < 5.

14. Continued: Check It Out Example 3 Graph the common solutions.