1. Tues, 2/14 SWBAT… solve compound inequalities Happy Valentine’s Day! Agenda 1. WU (10 min) 2. Review compound inequalities HW#3 and HW#4 (20 min) 3. Graphing inequalities: 10 examples - (15 min) Warm-Up: HW#5: Graphing Inequalities

2. HW#2 Answers 1. b ≥ -2 2. a < 3 3. m ≤ -40 4. w > 56 5. a ≥ 1 6. h < -15 7. b ≤ -1 8. No Solution 9. All Real Numbers 10. a < 2 11. x > 7 12. s > 37,000 13. t < 4 14. Ana is correct, Laura flipped the sign. 15. The first one does not belong (y > -3 instead of y > 3.)

3. HW#3 Answers 1. f < 11 and f ≥ 6 2. n ≤ -7 and n ≥ -12 3. y ≥ 8 or y < -4 4. t ≥ 1 or t < 19 5. -4 < p ≤ 5 6. -1 ≤ c < 2 7. h ≥ 2 and h < 3 8. m ≤ 6 or m ≥ 6 – Infinite Solutions (All real numbers) 9. a ≤ -4 and a > 4 – No Solution (Empty Set) 10. a ≤ ½ and a > 3 – No Solution (Empty Set) 11. n > -4 and n ≤ 3 12. n < 7 or n ≥ 11 13. n ≤ -4 or n > 1 14. n ≥ 0 and n < 3

4. ChemistryThe acidity of the water in a swimming pool is considered normal if the average of three pH readings is between 7.2 and 7.8. The first two readings for the swimming pool are 7.4 and 7.9. What possible values for the third reading p will make the average pH normal?

5. The value for the third reading must be between 6.3 and 8.1, inclusive.

6. GEOMETRYThe Triangle Inequality Theorem states that the sum of the measures of any two sides of a triangle is greater than the measure of the third side. a.) Write and solve three inequalities to express the relationships among the measures of the sides of the triangle shown above. b.) What are the possible lengths for the third side of the triangle? c.) Write a compound inequality for the possible values of x. 9 x 4

7. Set up your Cornell Notes… Topic is “Absolute Value Inequalities”

8. HW#5-Absolute Value Inequalities Answers 1. -24 < x < 8 2. -3 ≤ r ≤ 1 3. -3 ≤ c ≤ 4 4. -3 < h < 5 5. No Solution, Ø 6. All Real Numbers 7. r 4 8. k 7 9. p ≥ 22 or p ≤ -14 10. │p – 7.5│ ≤ 0.3

9. Thurs, 2/16 SWBAT… graph linear inequalities with two variables Agenda 1. Review HW#5 (15 min) 2. Graphing inequalities: 3 examples - (15 min) 3. Due at the end of the period: back of this weeks agenda (15 min) HW#5: Graphing Inequalities

10. Set up your Cornell Notes… Topic is “Graphing Linear Inequalities with two variables”

11. Graph -y – x < 2 Step 2: Graph the equality y > -x – 2 Step 3: Because y > -x – 2 and not ≥, the line will be dotted Step 4: Now shade the side of the line where y > -x - 2 (above the line). Step 1: Solve the inequality for y: y > -x – 2

12. Graphing a Linear Inequality Step 1) Solve the inequality for y (or for x if there is no y). Caution: You might need to flip the inequality sign if you multiply or divide by a negative # Step 2) Graph like before (begin with the b, move the m) Step 3) If the inequality is (not equals), the line is dashed (- - - - - - ). If the inequality is ≤ or ≥, the line is solid (______). Step 4) If the inequality is < or ≤, you shade below or to the left of the line. If the inequality is > or ≥, you shade above or to the right of the line.

13. Step 1: Solve the inequality for y: y ≤ 2x+1 Step 2: Graph the line y ≤ 2x + 1 Step 3: Because y ≤ 2x+1 and not <, the line will be solid Step 4: Now shade the side of the line where y < 2x+1 (below the line). Graph: y – 2x ≤ 1

14. Graph: 3 – x > 0 Step 1: Solve the inequality for x 3 - x > 0 -x > -3 x < 3 Step 2: Graph the line x = 3 Step 3: Because x < 3, the line will be dotted Step 4: Now shade the side of the line where x < 3 (to the left of the line) 6 4 2 3

15. Fri, 2/17 SWBAT… graph a system of linear inequalities Agenda 1. WU (10 min) 2. Finish HW#7 (10 min) 3. Graphing systems of linear inequalities: 1 example - (15 min) 3. Finish HW#8 Warm-Up: 1. Re-do correctly the problems that are circled on the back of this week’s agenda. 2. HW#9: Absolute Value & Inequalities Study Guide

16. HW#6 1. y < 2/3x – 2 2. x < 2 3. y > x + 2 y < -x + 1 4. y ≥ –x + 2 y ≥ 2 5. y > x y > -1/2x + 2 6. y ≥ 2x – 6 y ≥ -3/2x + 6

17. 1.) Given the inequality graphed below: a.) Write an inequality statement. b.) Name one ordered pair that is not in the solution set. c.) Name one ordered pair that is in the solution set.

18. 2. Given the inequality graphed below: a.) Write an inequality statement. b.) Name one ordered pair that is not in the solution set. c.) Name one ordered pair that is in the solution set.

19. 3.) Write a system of inequalities for the dark blue solution shown on the graph below. (Hint: you should write 2 different inequalities – one for each graph)

20. 4.) Write a system of inequalities for the green solution shown on the graph below. (Hint: you should write 2 different inequalities – one for each graph)

21. 5.) Write a system of inequalities for the dark blue solution shown on the graph below. (Hint: you should write 2 different inequalities – one for each graph)

22. 6.) Write a system of inequalities for the dark blue solution shown on the graph below. (Hint: you should write 2 different inequalities – one for each graph)

23. 7.) Write a system of inequalities for the blue solution shown on the graph below. (Hint: you should write 3 different inequalities – one for each graph)

24. SWBAT… graph systems of inequalities Tues, 2/21 Agenda 1. WU (10 min) 2. Review for Thursday’s test (35 min) WU: Complete on graph paper (collected) 1. Graph the inequality 6x – 3y ≥ 12. 2. Solve the following system of inequalities by graphing: -2x + y < -3 -3y + 6 ≤ 2x Prepare for Thursday’s test

25. Graphing Systems of Inequalities Choose a test point to determine which side of the line needs to be shaded. The test point for this problem was (0,0). Always pick a point that is easy to work with. 0 < 2(0) – 3 False 0 ≥ (-2/3)0 + 2 False Since both equations were false, shading occurred on the other side of the line, not covering the test point. The solution, S, is where the two shadings overlap one another.

26. Solution: Let x = the number of weekend ads Let y = the number of weekday ads x + y < 20 (there will be at most 20 ads) 200x + 50y < 2200 (the cost of the ads at most $2200)

27. Review for Thursday’s Test You will be assigned a problem and you will have to show and explain to the class how you solved it (using the ELMO) You will then create a similar problem that the class will have to solve (have the answer ready)