10-4 Inequalities Learn to read and write inequalities and graph them on a number line.

10-4 Inequalities Vocabulary inequality algebraic inequality solution set compound inequality

10-4 Inequalities An inequality states that two quantities either are not equal or may not be equal. An inequality uses one of the following symbols:

10-4 Inequalities 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.

10-4 Inequalities Additional Example 1: Writing Inequalities 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 Write an inequality for each situation.

10-4 Inequalities 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

10-4 Inequalities Additional Example 2: Graphing Simple Inequalities Graph each inequality. A. n<3. A. a>=24

10-4 Inequalities Check It Out Example 2 Graph each inequality. A. n<-1 A. j<=0

10-4 Inequalities Additional Example 3A : Graphing Compound Inequalities Graph each compound inequality. A. m ≤ –2 or m > 1 Graph m ≤ –2. Graph m > 1.

10-4 Inequalities Continued: Example 3A Graph the common solutions.

10-4 Inequalities Additional Example 3B : Graphing Compound Inequalities A. -3 < b ≤ 0 Graph -3 < b. Graph b ≤ 0

10-4 Inequalities Continued: Example 3B Graph the common solutions.

10-4 Inequalities Check It Out Example 3 Graph each compound inequality. Graph x > 4 Graph x < 5.

10-4 Inequalities Continued: Check It Out Example 3 Graph the common solutions.