1. Objectives: 1. Graph linear equations on a number line. 2. Solve one-step linear inequalities Vocabulary: linear inequalities, equivalent inequalities Solving One-Step Linear Inequalities 6.1

2. Vocabulary: linear inequality – an inequality where the variable has a power of 1, but not in a denominator, square root or absolute value symbols (, >) Solving One-Step Linear Inequalities 6.1 x < 5x 2 < -1 x > 0 x = 4 x < -1 2x < -1 x > 5x |x| < 12

3. Vocabulary: linear inequality – an inequality with the variable has a power of 1, but not in a denominator, square root or absolute value symbols (, >) equivalent inequalities – inequalities that have same solutions Solving One-Step Linear Inequalities 6.1 x < 52x < 10x + 1 < 6

4. Vocabulary: linear inequality – an inequality with the variable has a power of 1, but not in a denominator, square root or absolute value symbols (, >) equivalent inequalities – inequalities that have same solutions The graph of a linear inequality in one variable is the set of points on a number line that are solutions on the inequality. Open vs. Closed Circle when graphing Solving One-Step Linear Inequalities 6.1

5. Graph the following inequalities on a number line: 1. x > 4 2. x < -6 3. x > 1 4. x < 7 Example 1 Graph Linear Inequalities 0 1234567891011-3-2-4-5-6-7-8-9-10-11 0 1234567891011-3-2-4-5-6-7-8-9-10-11 0 1234567891011-3-2-4-5-6-7-8-9-10-11 0 1234567891011-3-2-4-5-6-7-8-9-10-11

6. REVIEW --- Solving equations: x + 8 = 12-2x = 20 x – 12 = 10 Solving One-Step Linear Inequalities x = 4x = -10 x = 22 x = -35 x = 12

7. What is the rule concerning multiplying and dividing on both sides of an inequality? Inequality Rule: Multiply or divide by a negative, then switch the sign!

8. Solving Inequalities: x + 8 > 12-2x < 20 x – 12 < 10 Solving One-Step Linear Inequalities Inequality Rule: Multiply or divide by a negative, then switch the sign!

9. Solve the inequality and graph the solution: x + 5 > -42x < 14 -2x < -6 Example 2 Solve and Graph the Inequality

10. Example 3 Real Life Inequalities If you scored a 78% on your last test, write an inequality that shows what you have to score to do better on the next one.

11. You walk across a bridge and you see a boat full of people yet there isn't a single person on board. How is that possible? Tonight’s Homework: P. 337-338 #’s 22-23, 34-35, 46-49, 63-64

12. Objectives: 1. Solve multi-step linear inequalities 2. Set up and Solve linear inequalities in the Real World Vocabulary: none Solving Multi-Step Linear Inequalities 6.2

13. When solving equations you must balance both side. 1.Simplify both sides of the equation. 2.Put variable on 1 side. 3.Do the opposite operation to both sides. 1.Addition/Subtraction 2.Multiplication/Division 4.Check! FOLLOW SAME Rules for Inequalities Solving Equations with Variables on Both Sides 3.4 Inequality Rule: Multiply or divide by a negative, then switch the sign!

14. Solve and Graph the inequalities on a number line: -3x + 1 < 22-x + 1 < 3x + 21 Example 1 Graph Linear Inequalities

15. Solve: 2y – 5 = 7 Solve & Graph: 2y – 5 < 7 x = 6 Inequality Rule: Multiply or divide by a negative, then switch the sign! Solving Multi-Step Linear Inequalities 2y – 6 < 4y + 8 -3x – 7 > 11

16. Real Life Inequalities You start growing geraniums from seed and plan to sell potted plants for Mother’s day. It costs you $1.75 to pot and grow each plant. If you sell each plant for $3.25, how many plants will you need to sell if you want to make a profit of at least $150?

17. What five letter word becomes shorter when you add two letters to it? You are running in a street marathon and you overtake the person in 2nd place. What place are you now? Tonight’s Homework: P. 343 #’s 16-20, 26-27, 37

18. Objectives: 1. Solve compound inequalities 2. Set up and Solve linear inequalities in the Real World Vocabulary: compound inequalities, and, or Solving Compound Inequalities 6.3

19. Vocabulary: compound inequality – two inequalities connected by “and” or “or” and – must be both I want to buy a car that is fast and has a great sound system. Solving Compound Inequalities 6.3

20. Vocabulary: compound inequality – two inequalities connected by “and” or “or” or – must be at least one of them, but could be both I want to buy a car that is red or a convertible. Solving Compound Inequalities 6.3

21. Write an inequality that represents the set of numbers and then graph it. Numbers that are less than -1 or greater than 2 Numbers that are less than or equal to -3 or greater than 0. 0 1234567891011-3-2-4-5-6-7-8-9-10-11 0 1234567891011-3-2-4-5-6-7-8-9-10-11 x 2 Example 1 Writing Compound Inequalities

22. Write an inequality that represents the set of numbers and then graph it. Numbers that are greater than 0 and less than or equal to 4. Numbers that are greater than or equal to -2 and less than 3. Writing Compound Inequalities 0 1234567891011-3-2-4-5-6-7-8-9-10-11 0 1234567891011-3-2-4-5-6-7-8-9-10-11

23. Solve the inequality and graph it. 1. -5 < 2x + 3 < 7 2. -2 < 3x – 8 < 10 Solving a Compound Inequality with “And” -4 < x < 2 0 1234567891011-3-2-4-5-6-7-8-9-10-11 0 1234567891011-3-2-4-5-6-7-8-9-10-11

24. Solve the inequality and graph it. 1. -2 < -2 – x < 1 2. -3 < -1 – 2x < 5 Solving a Compound Inequality with “And” 0 ≥ x > -3 or -3 < x ≤ 0 0 1234567891011-3-2-4-5-6-7-8-9-10-11 0 1234567891011-3-2-4-5-6-7-8-9-10-11

25. Solve the inequality and graph it. 1. 3x + 1 7 2. 6x – 5 25 Solving a Compound Inequality with “Or” x 6 0 1234567891011-3-2-4-5-6-7-8-9-10-11 0 1234567891011-3-2-4-5-6-7-8-9-10-11

26. Write and Graph an inequality that describes each condition. Water is a non-liquid when the temperature is 32°F or below or at least 212°F. A refrigerator is designed to work on an electric line carrying from 115 volts to 120 volts. Example 2 Writing Compound Inequalities

27. You throw away the outside and cook the inside. You eat the outside and throw away the inside. What did you eat? Tonight’s Homework: P. 349 #’s 12-14, 26-31

28. Objectives: 1. Solve absolute value equations 2. Solve absolute value inequalities Vocabulary: absolute value Solving Absolute Value Equations and Inequalities 6.4

29. Solving Absolute Value Equations and Inequalities 6.4 Simplify these expressions: |-5| |-4 - 7| |2(3 – 8)|

30. Solving Absolute Value Equations and Inequalities 6.4 Simplify this expression: = 8 x

31. Solving Absolute Value Equations and Inequalities 6.4 Simplify these expression: = 12 Solving Absolute Equations: 1.Isolate the absolute value. 2.Break it into 2 problems – one positive and the other negative. 3.Solve both equations. 4.Check both answers. x + 4

32. Solve these equations: Solving an Absolute Value Equation |6x - 3|=15 |2x - 8|= - 24 Solving Absolute Equations: 1.Isolate the absolute value. 2.Break it into 2 problems – one positive and the other negative. 3.Solve both equations. 4.Check both answers.

33. Solve these inequalities: Solving an Absolute Value Inequality |x|< 5 |x|< 4 |x|> 2 |x|> 6 Solving Absolute Inequalities: 1.Isolate the absolute value. 2.Break it into 2 problems – one positive and the other negative reversing the sign. 3.Solve both inequalities. 4.Check both answers. Absolute inequality rules: |x|< c, then –c < x < c “and” |x|> c, then x c “or”

34. Solve these inequalities: Solving an Absolute Value Inequality |x|< 5 |x|> 6 Solving Absolute Inequalities: 1.Isolate the absolute value. 2.Break it into 2 problems – one positive and the other negative reversing the sign. 3.Solve both inequalities. 4.Check both answers. Absolute inequality rules: |x|< c, then –c < x < c “and” |x|> c, then x c “or”

35. Solve these inequalities: Solving an Absolute Value Inequality Solving Absolute Inequalities: 1.Isolate the absolute value. 2.Break it into 2 problems – one positive and the other negative reversing the sign. 3.Solve both inequalities. 4.Check both answers. Absolute inequality rules: |x|< c, then –c < x < c “and” |x|> c, then x c “or” |4x - 9| < 21 |3x - 2| > 18

36. A small defenseless animal lays on the ground in the heat of the sun. Suddenly, it is pulled up and beaten with sticks. The animal's body is broken, but no one is punished for the crime. Why not? An electric train is going 40 mph north, the wind is blowing 60 mph south. Which way is the train's smoke blowing? Tonight’s Homework: P. 356-357 #’s 20-24, 40-42

37. Objectives: 1. Graph linear inequalities 2. Linear inequalities from real life Vocabulary: none Graphing Linear Inequalities in Two Variables 6.5

38. slope-intercept form  y = mx + b  great for graphing 1. Write Equation in Function Form 2. Plot the y-intercept (b) 3. Plot 1-2 more points using slope (m) When Graphing Linear Inequalities… uses DASHED LINE ≤ or ≥ uses SOLID LINE Graphing Linear Inequalities in Two Variables 6.5

39. Steps used when Graphing a Linear Inequality 1.Graph the line using best method 2.Use the correct boundary < or > dashed line (open circle) < or > solid line (closed circle) 3.SHADING - Color the good region– pick a point (0, 0) --- Shading can also be done using mental math!

40. Graphing a Linear Inequality

41. y < 2x

42. Graphing a Linear Inequality x > 4

43. Graphing a Linear Inequality 5x – 4y < 12

44. You have 30ft of fencing that you can use to enclose a rectangular sandbox. What are the possible dimensions. Display the results with a graph. Real Life Inequalities

45. You walk into a room with a match. In the room there is a stove, a heater and a candle. What do you light first? Tonight’s Homework: Worksheet 6.5 #’s 1-6

46. Objectives: 1. Graph systems of linear inequalities 2. Linear inequalities from real life Vocabulary: none Solving Systems of Linear Inequalities 7.6

47. Solve the System by Graphing Solve the system by graphing. 12 345 67 8 910 1 2 3 5 6 4 7 8 9 -6 -4-2 -8 -6 -2 -4 -8 (3, 4) Solve a System by Graphing 1.Graph both equations. 2.Find the intersection. 3.Check the answer.

48. Solve the System by Graphing Solve the system by graphing. 12 345 67 8 910 1 2 3 5 6 4 7 8 9 -6 -4-2 -8 -6 -2 -4 -8 (3, 4) Graph a System of Inequalities 1.Graph both inequalities. 2.Find the intersection. 3.Check a solution.

49. Solve the system by graphing. 12 345 67 8 910 1 2 3 5 6 4 7 8 9 -6 -4-2 -8 -6 -2 -4 -8 Graph a System of Inequalities 1.Graph both inequalities. 2.Find the intersection. 3.Check a solution.

50. Solve the system by graphing. 12 345 67 8 910 1 2 3 5 6 4 7 8 9 -6 -4-2 -8 -6 -2 -4 -8 Graph a System of Inequalities 1.Graph both inequalities. 2.Find the intersection. 3.Check a solution.

51. 12 345 67 8 910 1 2 3 5 6 4 7 8 9 -6 -4-2 -8 -6 -2 -4 -8 Solve the system by graphing. Graph a System of Inequalities 1.Graph both inequalities. 2.Find the intersection. 3.Check a solution.

52. 12 345 67 8 910 1 2 3 5 6 4 7 8 9 -6 -4-2 -8 -6 -2 -4 -8 Solve the system by graphing. Example 1 Graph a System of Inequalities 1.Graph both inequalities. 2.Find the intersection. 3.Check a solution.

53. My first is simply a vegetable, delicious, round and green. My third and fourth are sound asleep, as plainly can be seen. My fifth is fifty, clear enough for any riddle-setter. Two of my second stacked on their sides will give my final letter. Now that my second has my parts, fit them together well. You see me now before your eyes; it's plain for all to tell. Tonight’s Homework: Worksheet 7.6 #’s 1-4

54. Answer Puzzle. My first is simply a vegetable, delicious, round and green. - Pea / P My third and fourth are sound asleep, as plainly can be seen. - ZZ My fifth is fifty, clear enough for any riddle-setter. - L (Roman Numeral) Two of my second on their sides will give my final letter. - E (Take 2 U's and stack them sideways.) Now that my second has my parts, fit them together well. - Now that YOU (u) have my parts... You see me now before your eyes; it's plain for all to tell.