Chapter 5
Linear Inequalities
Section 5-1
Solving Inequalities by Addition and Subtraction
Essential Question
How do you solve and graph inequalities with
addition and subtraction?
Vocabulary
1. Set-builder notation:
Vocabulary
1. Set-builder notation: A mathematical way of writing the solution to
an inequality
Vocabulary
1. Set-builder notation: A mathematical way of writing the solution to
an inequality
x | x ≤ 7{ }
Vocabulary
1. Set-builder notation: A mathematical way of writing the solution to
an inequality
x | x ≤ 7{ }
“The set of x...
Notations
<
>
≤
≥
Notations
<
>
≤
≥
“Less than”
Notations
<
>
≤
≥
“Less than” Open end point
Notations
<
>
≤
≥
“Less than” Open end point Shade to the left
Notations
<
>
≤
≥
“Less than” Open end point Shade to the left
“Greater than”
Notations
<
>
≤
≥
“Less than” Open end point Shade to the left
“Greater than” Open end point
Notations
<
>
≤
≥
“Less than” Open end point Shade to the left
“Greater than” Open end point Shade to the right
Notations
<
>
≤
≥
“Less than” Open end point Shade to the left
“Greater than” Open end point Shade to the right
“Less than...
Notations
<
>
≤
≥
“Less than” Open end point Shade to the left
“Greater than” Open end point Shade to the right
“Less than...
Notations
<
>
≤
≥
“Less than” Open end point Shade to the left
“Greater than” Open end point Shade to the right
“Less than...
Notations
<
>
≤
≥
“Less than” Open end point Shade to the left
“Greater than” Open end point Shade to the right
“Less than...
Notations
<
>
≤
≥
“Less than” Open end point Shade to the left
“Greater than” Open end point Shade to the right
“Less than...
Notations
<
>
≤
≥
“Less than” Open end point Shade to the left
“Greater than” Open end point Shade to the right
“Less than...
Example 1
Solve the inequality. Write your solution in set-builder notation.
Graph your solution.
c −12 > 65
Example 1
Solve the inequality. Write your solution in set-builder notation.
Graph your solution.
c −12 > 65
+12
Example 1
Solve the inequality. Write your solution in set-builder notation.
Graph your solution.
c −12 > 65
+12 +12
Example 1
Solve the inequality. Write your solution in set-builder notation.
Graph your solution.
c −12 > 65
+12 +12
Example 1
Solve the inequality. Write your solution in set-builder notation.
Graph your solution.
c −12 > 65
+12 +12
c > 77
Example 1
Solve the inequality. Write your solution in set-builder notation.
Graph your solution.
c −12 > 65
+12 +12
c > 7...
Example 1
Solve the inequality. Write your solution in set-builder notation.
Graph your solution.
c −12 > 65
+12 +12
c > 7...
Example 1
Solve the inequality. Write your solution in set-builder notation.
Graph your solution.
c −12 > 65
+12 +12
c > 7...
Example 1
Solve the inequality. Write your solution in set-builder notation.
Graph your solution.
c −12 > 65
+12 +12
c > 7...
Example 1
Solve the inequality. Write your solution in set-builder notation.
Graph your solution.
c −12 > 65
+12 +12
c > 7...
Example 2
Solve the inequality. Write your solution in set-builder notation.
Graph your solution.
x + 23 <14
Example 2
Solve the inequality. Write your solution in set-builder notation.
Graph your solution.
x + 23 <14
−23
Example 2
Solve the inequality. Write your solution in set-builder notation.
Graph your solution.
x + 23 <14
−23 −23
Example 2
Solve the inequality. Write your solution in set-builder notation.
Graph your solution.
x + 23 <14
−23 −23
Example 2
Solve the inequality. Write your solution in set-builder notation.
Graph your solution.
x + 23 <14
−23 −23
x < −9
Example 2
Solve the inequality. Write your solution in set-builder notation.
Graph your solution.
x + 23 <14
−23 −23
x < −...
Example 2
Solve the inequality. Write your solution in set-builder notation.
Graph your solution.
x + 23 <14
−23 −23
x < −...
Example 2
Solve the inequality. Write your solution in set-builder notation.
Graph your solution.
x + 23 <14
−23 −23
x < −...
Example 2
Solve the inequality. Write your solution in set-builder notation.
Graph your solution.
x + 23 <14
−23 −23
x < −...
Example 2
Solve the inequality. Write your solution in set-builder notation.
Graph your solution.
x + 23 <14
−23 −23
x < −...
Example 3
Solve the inequality. Write your solution in set-builder notation.
Graph your solution.
12n − 4 ≤13n
Example 3
Solve the inequality. Write your solution in set-builder notation.
Graph your solution.
12n − 4 ≤13n
+4
Example 3
Solve the inequality. Write your solution in set-builder notation.
Graph your solution.
12n − 4 ≤13n
+4 +4
Example 3
Solve the inequality. Write your solution in set-builder notation.
Graph your solution.
12n − 4 ≤13n
+4 +4−13n
Example 3
Solve the inequality. Write your solution in set-builder notation.
Graph your solution.
12n − 4 ≤13n
+4 +4−13n−1...
Example 3
Solve the inequality. Write your solution in set-builder notation.
Graph your solution.
12n − 4 ≤13n
+4 +4−13n−1...
Example 3
Solve the inequality. Write your solution in set-builder notation.
Graph your solution.
12n − 4 ≤13n
+4 +4
−n ≤ ...
Example 3
Solve the inequality. Write your solution in set-builder notation.
Graph your solution.
12n − 4 ≤13n
+4 +4
−n ≤ ...
Example 3
Solve the inequality. Write your solution in set-builder notation.
Graph your solution.
12n − 4 ≤13n
+4 +4
−n ≤ ...
Example 3
Solve the inequality. Write your solution in set-builder notation.
Graph your solution.
12n − 4 ≤13n
+4 +4
−n ≤ ...
Example 3
Solve the inequality. Write your solution in set-builder notation.
Graph your solution.
12n − 4 ≤13n
+4 +4
−n ≤ ...
Example 3
Solve the inequality. Write your solution in set-builder notation.
Graph your solution.
12n − 4 ≤13n
+4 +4
−n ≤ ...
Example 3
Solve the inequality. Write your solution in set-builder notation.
Graph your solution.
12n − 4 ≤13n
+4 +4
−n ≤ ...
Example 3
Solve the inequality. Write your solution in set-builder notation.
Graph your solution.
12n − 4 ≤13n
+4 +4
−n ≤ ...
Example 4
Matt Mitarnowski wants to buy season passes to two theme parks. If one
season pass is $54.99 (tax included) and ...
Example 4
Matt Mitarnowski wants to buy season passes to two theme parks. If one
season pass is $54.99 (tax included) and ...
Example 4
Matt Mitarnowski wants to buy season passes to two theme parks. If one
season pass is $54.99 (tax included) and ...
Example 4
Matt Mitarnowski wants to buy season passes to two theme parks. If one
season pass is $54.99 (tax included) and ...
Example 4
Matt Mitarnowski wants to buy season passes to two theme parks. If one
season pass is $54.99 (tax included) and ...
Example 4
Matt Mitarnowski wants to buy season passes to two theme parks. If one
season pass is $54.99 (tax included) and ...
Example 4
Matt Mitarnowski wants to buy season passes to two theme parks. If one
season pass is $54.99 (tax included) and ...
Example 4
Matt Mitarnowski wants to buy season passes to two theme parks. If one
season pass is $54.99 (tax included) and ...
Summarizer
Compare and contrast the following graphs.
a < 4 a ≤ 4
Problem Sets
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...
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Algebra 1B Section 5-1

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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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