1. Chapter 4.1-4.2 Notes: Solving Inequalities Using Addition, Subtraction, Multiplication and Division Goal: You will solve inequalities using addition, subtraction, multiplication, and division.

2. Graphing an Inequality On a number line, the graph of an inequality in one variable is the set of points that represent all solutions of the inequality. To graph an inequality in one variable, use an open circle for and a closed circle for ≤ or ≥. i.e. Graph x < 3 i.e. Graph x ≥ -1 Ex.1: Graph x ≤ -2 Ex.2: Graph x > 8

3. Ex.3: Write an inequality represented by the graph. a. b. c. d.

4. Equivalent Inequalities Equivalent inequalities are inequalities that have the same solution. Adding and Subtracting Inequalities: Ex.4: Solve x – 5 > -3.5. Graph your solution. Solve the inequality. Graph your solution. Ex.5: x – 9 ≤ 3 Ex.6: p – 9.2 < -5

5. Ex.7: Solve 9 ≥ x + 7 Solve the inequality. Graph your solution. Ex.8: -2 < y + 15 Ex.9: x + 7 ≥ -4 Multiplying and Dividing Inequalities When multiplying or dividing each side of an inequality by a negative number, you will ALWAYS reverse the direction of the inequality symbol.

6. Ex.10: Solve < 5. Graph your solution. Ex.11: Solve < 7. Graph your solution. Ex.12: Solve -3x > 24. Graph your solution. Ex.13: Solve -6x ≤ 18. Graph your solution.

7. Solve the inequality. Graph your solution. Ex.14: 5v ≥ 45 Ex.15: 28 > -4y Ex.16: Ex.17: > 12 Ex.18: You are checking a bag at an airport. Bags can weigh no more than 50 pounds. Your bag weighs 16.8 pounds. Find the possible weights, w, (in possible) that you can add to the bag.

8. Ex.19: You are shopping for bicycles. The type you want costs at least $185. You have saved $97. Find the possible amounts of money to save to buy the bicycles you want. Ex.20: A student pilot plans to spend 80 hours on flight training to earn a private license. The student has saved $6000 for training. What are the possible hourly rates that the student can afford to pay for training?

9. Ex.21: A restaurant owner plans to place identical bouquets of flowers on 35 tables for opening night. The owner wants to spend no more than $400 for all the bouquets. What are the possible amounts of money the owner should budget for each bouquet of flowers?