1. Using Addition and Subtraction to Solve 2.9 p. 106 Solving Inequalities

2. What is the objective? We will combine the processes from solving addition and subtraction equations with graphing linear inequalities We will solve these inequalities and graph the solutions As both these skills are review, the PROCESS and INTEGER RULES should be the focus.

3. Properties of Inequalities Algebraically….this means If a ≥ bIf a ≤ b a + 3 ≥ b + 3 then a + 3 ≤ b + 3 Suppose a = 5 and b = 3 Then (5 + 3) is greater than (3 + 3) 8 > 3 If a ≥ bIf a ≤ b a + 3 ≥ b + 3 then a + 3 ≤ b + 3 Suppose a = 5 and b = 3 Then (5 + 3) is greater than (3 + 3) 8 > 3 Note info starts on the next slide.

4. Solution Examples For inequalities involving only addition and subtraction, solve as if these were equations. n + 8 ≥ 19 -8 - 8 n ≥ 11 For inequalities involving only addition and subtraction, solve as if these were equations. n + 8 ≥ 19 -8 - 8 n ≥ 11 111210 If a > b If a < b a + c > b + c a – c < b - c

5. WAIT!!! Listen to the values! n + 8 ≥ 19 $$ + $8 gives me $19 or more than $19 Inequalities are just another neat way to communicate mathematically. Here is what this inequality is saying to you…..”You had some money, and someone gave you another $8. You now have at least $19. The “n” represents the range of $$$$$ you started with. Our solution, n ≥ 11 tells us that we could have started with $11. This would give us a total of $19. Or we could have started with MORE than $11. This would have made the final amount more than $19. 111210

6. Watch the Signs! -26 > y + 14 You should see the importance of -14 -14 leaving the variable on the same side! -40 > y You will solve and graph several inequalities. Show all work. Create a graph for each solution. -26 > y + 14 You should see the importance of -14 -14 leaving the variable on the same side! -40 > y You will solve and graph several inequalities. Show all work. Create a graph for each solution. -40-39-41

7. Practice p. 106 m + 3 > 68 + t < 15 -3 ≤ n + 7 -3 m > 3 2 3 4 -8 t < 7 6 7 8 -11 -10 -9 -7 -10 ≤ n

8. Application An airline lets you check up to 65 lb. of luggage with no extra fee. One suitcase weighs 37 lb. What is the most the second suitcase can weigh? You are writing an inequality BEFORE you solve! 1 st + 2 nd bag can be no more than 65 37 + b ≤ 65 -37 b ≤ 28 The second bag can weigh no more than 28 pounds.

9. Using Addition to Solve We will solve first, then we will graph. n - 15 29 7 ≥ v - 4 11 ≤ t - 5 + 15 + 15 n < 18 + 13 +13 m > 42 +4 +4 11 ≥ v + 5 +5 16 ≤ t 17 18 19 41 42 43 10 11 12 15 16 17

10. What was our objective? We combined the processes from solving addition and subtraction equations with graphing linear inequalities We solved these inequalities and graphed the solutions The PROCESS and INTEGER RULES were the focus.

11. That’s All Folks!