Alg1bsection5 1slidenotes-130917185603-phpapp01
- 2. Section 5-1 Solving Inequalities by Addition and Subtraction
- 3. Essential Question How do you solve and graph inequalities with addition and subtraction?
- 5. Vocabulary 1. Set-builder notation: A mathematical way of writing the solution to an inequality
- 6. Vocabulary 1. Set-builder notation: A mathematical way of writing the solution to an inequality x | x ≤ 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”
- 10. Notations < > ≤ ≥ “Less than” Open end point
- 11. Notations < > ≤ ≥ “Less than” Open end point Shade to the left
- 12. Notations < > ≤ ≥ “Less than” Open end point Shade to the left “Greater than”
- 13. Notations < > ≤ ≥ “Less than” Open end point Shade to the left “Greater than” Open end point
- 14. Notations < > ≤ ≥ “Less than” Open end point Shade to the left “Greater than” Open end point Shade to the right
- 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. 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. 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. 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. 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. 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. Example 1 Solve the inequality. Write your solution in set-builder notation. Graph your solution. c −12 > 65
- 22. Example 1 Solve the inequality. Write your solution in set-builder notation. Graph your solution. c −12 > 65 +12
- 23. Example 1 Solve the inequality. Write your solution in set-builder notation. Graph your solution. c −12 > 65 +12 +12
- 24. Example 1 Solve the inequality. Write your solution in set-builder notation. Graph your solution. c −12 > 65 +12 +12
- 25. Example 1 Solve the inequality. Write your solution in set-builder notation. Graph your solution. c −12 > 65 +12 +12 c > 77
- 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. 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. 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. 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. 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. Example 2 Solve the inequality. Write your solution in set-builder notation. Graph your solution. x + 23 <14
- 32. Example 2 Solve the inequality. Write your solution in set-builder notation. Graph your solution. x + 23 <14 −23
- 33. Example 2 Solve the inequality. Write your solution in set-builder notation. Graph your solution. x + 23 <14 −23 −23
- 34. Example 2 Solve the inequality. Write your solution in set-builder notation. Graph your solution. x + 23 <14 −23 −23
- 35. Example 2 Solve the inequality. Write your solution in set-builder notation. Graph your solution. x + 23 <14 −23 −23 x < −9
- 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. 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. 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. 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. 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. Example 3 Solve the inequality. Write your solution in set-builder notation. Graph your solution. 12n − 4 ≤13n
- 42. Example 3 Solve the inequality. Write your solution in set-builder notation. Graph your solution. 12n − 4 ≤13n +4
- 43. Example 3 Solve the inequality. Write your solution in set-builder notation. Graph your solution. 12n − 4 ≤13n +4 +4
- 44. Example 3 Solve the inequality. Write your solution in set-builder notation. Graph your solution. 12n − 4 ≤13n +4 +4−13n
- 45. Example 3 Solve the inequality. Write your solution in set-builder notation. Graph your solution. 12n − 4 ≤13n +4 +4−13n−13n
- 46. Example 3 Solve the inequality. Write your solution in set-builder notation. Graph your solution. 12n − 4 ≤13n +4 +4−13n−13n
- 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. Summarizer Compare and contrast the following graphs. a < 4 a ≤ 4
- 64. Problem Sets
- 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