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# Algebra 1B Section 5-1

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Linear Inequalities

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### Algebra 1B Section 5-1

1. 1. Chapter 5 Linear Inequalities
2. 2. Section 5-1 Solving Inequalities by Addition and Subtraction
3. 3. Essential Question How do you solve and graph inequalities with addition and subtraction?
4. 4. Vocabulary 1. Set-builder notation:
5. 5. Vocabulary 1. Set-builder notation: A mathematical way of writing the solution to an inequality
6. 6. Vocabulary 1. Set-builder notation: A mathematical way of writing the solution to an inequality x | x ≤ 7{ }
7. 7. Vocabulary 1. Set-builder notation: A mathematical way of writing the solution to an inequality x | x ≤ 7{ } “The set of x such that x is less than or equal to seven”
8. 8. Notations < > ≤ ≥
9. 9. Notations < > ≤ ≥ “Less than”
10. 10. Notations < > ≤ ≥ “Less than” Open end point
11. 11. Notations < > ≤ ≥ “Less than” Open end point Shade to the left
12. 12. Notations < > ≤ ≥ “Less than” Open end point Shade to the left “Greater than”
13. 13. Notations < > ≤ ≥ “Less than” Open end point Shade to the left “Greater than” Open end point
14. 14. Notations < > ≤ ≥ “Less than” Open end point Shade to the left “Greater than” Open end point Shade to the right
15. 15. Notations < > ≤ ≥ “Less than” Open end point Shade to the left “Greater than” Open end point Shade to the right “Less than or equal to”
16. 16. Notations < > ≤ ≥ “Less than” Open end point Shade to the left “Greater than” Open end point Shade to the right “Less than or equal to” Closed end point
17. 17. Notations < > ≤ ≥ “Less than” Open end point Shade to the left “Greater than” Open end point Shade to the right “Less than or equal to” Closed end point Shade to the left
18. 18. Notations < > ≤ ≥ “Less than” Open end point Shade to the left “Greater than” Open end point Shade to the right “Less than or equal to” Closed end point Shade to the left “Greater than or equal to”
19. 19. Notations < > ≤ ≥ “Less than” Open end point Shade to the left “Greater than” Open end point Shade to the right “Less than or equal to” Closed end point Shade to the left “Greater than or equal to” Closed end point
20. 20. Notations < > ≤ ≥ “Less than” Open end point Shade to the left “Greater than” Open end point Shade to the right “Less than or equal to” Closed end point Shade to the left “Greater than or equal to” Closed end point Shade to the right
21. 21. Example 1 Solve the inequality. Write your solution in set-builder notation. Graph your solution. c −12 > 65
22. 22. Example 1 Solve the inequality. Write your solution in set-builder notation. Graph your solution. c −12 > 65 +12
23. 23. Example 1 Solve the inequality. Write your solution in set-builder notation. Graph your solution. c −12 > 65 +12 +12
24. 24. Example 1 Solve the inequality. Write your solution in set-builder notation. Graph your solution. c −12 > 65 +12 +12
25. 25. Example 1 Solve the inequality. Write your solution in set-builder notation. Graph your solution. c −12 > 65 +12 +12 c > 77
26. 26. Example 1 Solve the inequality. Write your solution in set-builder notation. Graph your solution. c −12 > 65 +12 +12 c > 77 c | c > 77{ }
27. 27. Example 1 Solve the inequality. Write your solution in set-builder notation. Graph your solution. c −12 > 65 +12 +12 c > 77 c | c > 77{ }
28. 28. Example 1 Solve the inequality. Write your solution in set-builder notation. Graph your solution. c −12 > 65 +12 +12 c > 77 c | c > 77{ } 77 78 79 80 8176757473
29. 29. Example 1 Solve the inequality. Write your solution in set-builder notation. Graph your solution. c −12 > 65 +12 +12 c > 77 c | c > 77{ } 77 78 79 80 8176757473
30. 30. Example 1 Solve the inequality. Write your solution in set-builder notation. Graph your solution. c −12 > 65 +12 +12 c > 77 c | c > 77{ } 77 78 79 80 8176757473
31. 31. Example 2 Solve the inequality. Write your solution in set-builder notation. Graph your solution. x + 23 <14
32. 32. Example 2 Solve the inequality. Write your solution in set-builder notation. Graph your solution. x + 23 <14 −23
33. 33. Example 2 Solve the inequality. Write your solution in set-builder notation. Graph your solution. x + 23 <14 −23 −23
34. 34. Example 2 Solve the inequality. Write your solution in set-builder notation. Graph your solution. x + 23 <14 −23 −23
35. 35. Example 2 Solve the inequality. Write your solution in set-builder notation. Graph your solution. x + 23 <14 −23 −23 x < −9
36. 36. Example 2 Solve the inequality. Write your solution in set-builder notation. Graph your solution. x + 23 <14 −23 −23 x < −9 x | x < −9{ }
37. 37. Example 2 Solve the inequality. Write your solution in set-builder notation. Graph your solution. x + 23 <14 −23 −23 x < −9 x | x < −9{ }
38. 38. Example 2 Solve the inequality. Write your solution in set-builder notation. Graph your solution. x + 23 <14 −23 −23 x < −9 x | x < −9{ } -9 -8 -7 -6 -5-10-11-12-13
39. 39. Example 2 Solve the inequality. Write your solution in set-builder notation. Graph your solution. x + 23 <14 −23 −23 x < −9 x | x < −9{ } -9 -8 -7 -6 -5-10-11-12-13
40. 40. Example 2 Solve the inequality. Write your solution in set-builder notation. Graph your solution. x + 23 <14 −23 −23 x < −9 x | x < −9{ } -9 -8 -7 -6 -5-10-11-12-13
41. 41. Example 3 Solve the inequality. Write your solution in set-builder notation. Graph your solution. 12n − 4 ≤13n
42. 42. Example 3 Solve the inequality. Write your solution in set-builder notation. Graph your solution. 12n − 4 ≤13n +4
43. 43. Example 3 Solve the inequality. Write your solution in set-builder notation. Graph your solution. 12n − 4 ≤13n +4 +4
44. 44. Example 3 Solve the inequality. Write your solution in set-builder notation. Graph your solution. 12n − 4 ≤13n +4 +4−13n
45. 45. Example 3 Solve the inequality. Write your solution in set-builder notation. Graph your solution. 12n − 4 ≤13n +4 +4−13n−13n
46. 46. Example 3 Solve the inequality. Write your solution in set-builder notation. Graph your solution. 12n − 4 ≤13n +4 +4−13n−13n
47. 47. Example 3 Solve the inequality. Write your solution in set-builder notation. Graph your solution. 12n − 4 ≤13n +4 +4 −n ≤ 4 −13n−13n
48. 48. Example 3 Solve the inequality. Write your solution in set-builder notation. Graph your solution. 12n − 4 ≤13n +4 +4 −n ≤ 4 −13n−13n −1
49. 49. Example 3 Solve the inequality. Write your solution in set-builder notation. Graph your solution. 12n − 4 ≤13n +4 +4 −n ≤ 4 −13n−13n −1 −1
50. 50. Example 3 Solve the inequality. Write your solution in set-builder notation. Graph your solution. 12n − 4 ≤13n +4 +4 −n ≤ 4 n | n ≥ −4{ } −13n−13n −1 −1
51. 51. Example 3 Solve the inequality. Write your solution in set-builder notation. Graph your solution. 12n − 4 ≤13n +4 +4 −n ≤ 4 n | n ≥ −4{ } −13n−13n −1 −1
52. 52. Example 3 Solve the inequality. Write your solution in set-builder notation. Graph your solution. 12n − 4 ≤13n +4 +4 −n ≤ 4 n | n ≥ −4{ } -4 -3 -2 -1 0-5-6-7-8 −13n−13n −1 −1
53. 53. Example 3 Solve the inequality. Write your solution in set-builder notation. Graph your solution. 12n − 4 ≤13n +4 +4 −n ≤ 4 n | n ≥ −4{ } -4 -3 -2 -1 0-5-6-7-8 −13n−13n −1 −1
54. 54. Example 3 Solve the inequality. Write your solution in set-builder notation. Graph your solution. 12n − 4 ≤13n +4 +4 −n ≤ 4 n | n ≥ −4{ } -4 -3 -2 -1 0-5-6-7-8 −13n−13n −1 −1
55. 55. Example 4 Matt Mitarnowski wants to buy season passes to two theme parks. If one season pass is \$54.99 (tax included) and he has \$100 to spend on both passes, the second season pass must cost no more than what amount?
56. 56. Example 4 Matt Mitarnowski wants to buy season passes to two theme parks. If one season pass is \$54.99 (tax included) and he has \$100 to spend on both passes, the second season pass must cost no more than what amount? Let x be the cost of the second ticket
57. 57. Example 4 Matt Mitarnowski wants to buy season passes to two theme parks. If one season pass is \$54.99 (tax included) and he has \$100 to spend on both passes, the second season pass must cost no more than what amount? Let x be the cost of the second ticket x + 54.99 ≤100
58. 58. Example 4 Matt Mitarnowski wants to buy season passes to two theme parks. If one season pass is \$54.99 (tax included) and he has \$100 to spend on both passes, the second season pass must cost no more than what amount? Let x be the cost of the second ticket x + 54.99 ≤100 −54.99
59. 59. Example 4 Matt Mitarnowski wants to buy season passes to two theme parks. If one season pass is \$54.99 (tax included) and he has \$100 to spend on both passes, the second season pass must cost no more than what amount? Let x be the cost of the second ticket x + 54.99 ≤100 −54.99 −54.99
60. 60. Example 4 Matt Mitarnowski wants to buy season passes to two theme parks. If one season pass is \$54.99 (tax included) and he has \$100 to spend on both passes, the second season pass must cost no more than what amount? Let x be the cost of the second ticket x + 54.99 ≤100 −54.99 −54.99
61. 61. Example 4 Matt Mitarnowski wants to buy season passes to two theme parks. If one season pass is \$54.99 (tax included) and he has \$100 to spend on both passes, the second season pass must cost no more than what amount? Let x be the cost of the second ticket x + 54.99 ≤100 −54.99 −54.99 x ≤ 45.01
62. 62. Example 4 Matt Mitarnowski wants to buy season passes to two theme parks. If one season pass is \$54.99 (tax included) and he has \$100 to spend on both passes, the second season pass must cost no more than what amount? Let x be the cost of the second ticket x + 54.99 ≤100 −54.99 −54.99 x ≤ 45.01 The second ticket must be \$45.01 or less
63. 63. Summarizer Compare and contrast the following graphs. a < 4 a ≤ 4
64. 64. Problem Sets
65. 65. Problem Sets Problem Set 1: p. 286 #1-11 Problem Set 2: p.286 #12-27 multiples of 3, #30-40 all "I have found power in the mysteries of thought." - Euripides
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