1. GRAB YOUR NOTEBOOK AND LABEL THE NEXT BLANK PAGE UNIT 16. (If you have no room in your notebook, do the warm- up and notes on a piece of paper in a binder or folder) Warm Up Solve. 1.–21 + 12z = –27 2. –18 = –6n 3. 56 + x = 8 4. 9k - 9 = –18 n = 3 x = -48 Course 2 12-4 Inequalities k = -1

2. Learn to read and write inequalities and graph them on a number line. Course 2 12-4 Inequalities Homework: Kuta worksheet

3. An inequality states that two quantities either are not equal or may not be equal. An inequality uses one of the following symbols: SymbolMeaningWord Phrases < > ≤ ≥ is less than is greater than is greater than or equal to is less than or equal to Fewer than, below More than, above At most, no more than At least, no less than Course 2 12-4 Inequalities

4. Write an inequality for each situation. 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 Course 2 12-4 Inequalities

5. Write an inequality for each situation. Check It Out: Example 1 A. There are at most 10 gallons of gas in the tank. gallons of gas ≤ 10 B. There is at least 10 yards of fabric left. yards of fabric ≥ 10 Course 2 12-4 Inequalities

6. 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. You can graph the solutions of an inequality on a number line. If the variable is “greater than” or “less than” a number, then that number is indicated with an open circle. Course 2 12-4 Inequalities

7. This open circle shows that 5 is not a solution. a > 5 If the variable is “greater than or equal to” or “less than or equal to” a number, that number is indicated with a closed circle. This closed circle shows that 3 is a solution. b ≤ 3 Course 2 12-4 Inequalities

8. Graph each inequality. Additional Example 2: Graphing Simple Inequalities –3 –2 –1 0 1 2 3 A. n < 3 B. a ≥ –4 –6 –4 –2 0 2 4 6 Course 2 12-4 Inequalities

9. Graph each inequality. Check It Out: Example 2 –3 –2 –1 0 1 2 3 A. p ≤ 2 B. e > –2 –3 –2 –1 0 1 2 3 Course 2 12-4 Inequalities

10. Lesson Quiz: Part I Write an inequality for each situation. 1. No more than 220 people are in the theater. 2. There are at least a dozen eggs left. 3. Fewer than 14 people attended the meeting. number of eggs ≥ 12 people in the theater ≤ 220 Insert Lesson Title Here people attending the meeting < 14 Course 2 12-4 Inequalities

11. Lesson Quiz: Part II Graph the inequalities. 4. x > –1 Insert Lesson Title Here 0 º 135 123 – – – Course 2 12-4 Inequalities