Algebra 1B Section 5-3

  • 131 views
Uploaded on

Solving Multi-Step Inequalities

Solving Multi-Step Inequalities

  • Full Name Full Name Comment goes here.
    Are you sure you want to
    Your message goes here
    Be the first to comment
    Be the first to like this
No Downloads

Views

Total Views
131
On Slideshare
0
From Embeds
0
Number of Embeds
1

Actions

Shares
Downloads
4
Comments
0
Likes
0

Embeds 0

No embeds

Report content

Flagged as inappropriate Flag as inappropriate
Flag as inappropriate

Select your reason for flagging this presentation as inappropriate.

Cancel
    No notes for slide

Transcript

  • 1. SECTION 5-3 Solving Multi-Step Inequalities Monday, September 30, 13
  • 2. ESSENTIAL QUESTION • How do we solve multi-step inequalities? Monday, September 30, 13
  • 3. WARM UP 2x − 7 = 9 + 4xa. 1 2 a = a − 3 4 b. Monday, September 30, 13
  • 4. WARM UP 2x − 7 = 9 + 4xa. 1 2 a = a − 3 4 b. −2x Monday, September 30, 13
  • 5. WARM UP 2x − 7 = 9 + 4xa. 1 2 a = a − 3 4 b. −2x −2x Monday, September 30, 13
  • 6. WARM UP 2x − 7 = 9 + 4xa. 1 2 a = a − 3 4 b. −2x −2x−9 Monday, September 30, 13
  • 7. WARM UP 2x − 7 = 9 + 4xa. 1 2 a = a − 3 4 b. −2x −2x−9−9 Monday, September 30, 13
  • 8. WARM UP 2x − 7 = 9 + 4xa. 1 2 a = a − 3 4 b. −2x −2x−9−9 Monday, September 30, 13
  • 9. WARM UP 2x − 7 = 9 + 4xa. 1 2 a = a − 3 4 b. −2x −2x−9−9 −16 = 2x Monday, September 30, 13
  • 10. WARM UP 2x − 7 = 9 + 4xa. 1 2 a = a − 3 4 b. −2x −2x−9−9 −16 = 2x 22 Monday, September 30, 13
  • 11. WARM UP 2x − 7 = 9 + 4xa. 1 2 a = a − 3 4 b. −2x −2x−9−9 −16 = 2x 22 −8 = x Monday, September 30, 13
  • 12. WARM UP 2x − 7 = 9 + 4xa. 1 2 a = a − 3 4 b. −2x −2x−9−9 −16 = 2x 22 −8 = x x = −8 Monday, September 30, 13
  • 13. WARM UP 2x − 7 = 9 + 4xa. 1 2 a = a − 3 4 b. −2x −2x−9−9 −16 = 2x 22 −8 = x x = −8 4 • 1 2 a = a − 3 4 • 4 Monday, September 30, 13
  • 14. WARM UP 2x − 7 = 9 + 4xa. 1 2 a = a − 3 4 b. −2x −2x−9−9 −16 = 2x 22 −8 = x x = −8 4 • 1 2 a = a − 3 4 • 4 2a = a − 3 Monday, September 30, 13
  • 15. WARM UP 2x − 7 = 9 + 4xa. 1 2 a = a − 3 4 b. −2x −2x−9−9 −16 = 2x 22 −8 = x x = −8 4 • 1 2 a = a − 3 4 • 4 2a = a − 3 −a−a Monday, September 30, 13
  • 16. WARM UP 2x − 7 = 9 + 4xa. 1 2 a = a − 3 4 b. −2x −2x−9−9 −16 = 2x 22 −8 = x x = −8 4 • 1 2 a = a − 3 4 • 4 2a = a − 3 −a−a a = −3 Monday, September 30, 13
  • 17. EXAMPLE 1 Maggie Brann has a budget of $115 for faxes.The fax service she uses charges $25 to activate an account and $0.08 per page to send faxes. How many pages can she fax and stay within her budget? Identify a variable, then set up and solve an inequality. Interpret your solution. Monday, September 30, 13
  • 18. EXAMPLE 1 Maggie Brann has a budget of $115 for faxes.The fax service she uses charges $25 to activate an account and $0.08 per page to send faxes. How many pages can she fax and stay within her budget? Identify a variable, then set up and solve an inequality. Interpret your solution. p = pages she can fax Monday, September 30, 13
  • 19. EXAMPLE 1 Maggie Brann has a budget of $115 for faxes.The fax service she uses charges $25 to activate an account and $0.08 per page to send faxes. How many pages can she fax and stay within her budget? Identify a variable, then set up and solve an inequality. Interpret your solution. p = pages she can fax 25+ .08p ≤115 Monday, September 30, 13
  • 20. EXAMPLE 1 Maggie Brann has a budget of $115 for faxes.The fax service she uses charges $25 to activate an account and $0.08 per page to send faxes. How many pages can she fax and stay within her budget? Identify a variable, then set up and solve an inequality. Interpret your solution. p = pages she can fax 25+ .08p ≤115 −25 −25 Monday, September 30, 13
  • 21. EXAMPLE 1 Maggie Brann has a budget of $115 for faxes.The fax service she uses charges $25 to activate an account and $0.08 per page to send faxes. How many pages can she fax and stay within her budget? Identify a variable, then set up and solve an inequality. Interpret your solution. p = pages she can fax 25+ .08p ≤115 −25 −25 .08p ≤ 90 Monday, September 30, 13
  • 22. EXAMPLE 1 Maggie Brann has a budget of $115 for faxes.The fax service she uses charges $25 to activate an account and $0.08 per page to send faxes. How many pages can she fax and stay within her budget? Identify a variable, then set up and solve an inequality. Interpret your solution. p = pages she can fax 25+ .08p ≤115 −25 −25 .08p ≤ 90 .08 .08 Monday, September 30, 13
  • 23. EXAMPLE 1 Maggie Brann has a budget of $115 for faxes.The fax service she uses charges $25 to activate an account and $0.08 per page to send faxes. How many pages can she fax and stay within her budget? Identify a variable, then set up and solve an inequality. Interpret your solution. p = pages she can fax 25+ .08p ≤115 −25 −25 .08p ≤ 90 .08 .08 p ≤1125 Monday, September 30, 13
  • 24. EXAMPLE 1 Maggie Brann has a budget of $115 for faxes.The fax service she uses charges $25 to activate an account and $0.08 per page to send faxes. How many pages can she fax and stay within her budget? Identify a variable, then set up and solve an inequality. Interpret your solution. p = pages she can fax 25+ .08p ≤115 −25 −25 .08p ≤ 90 .08 .08 p ≤1125 p | p ≤1125{ } Monday, September 30, 13
  • 25. EXAMPLE 1 Maggie Brann has a budget of $115 for faxes.The fax service she uses charges $25 to activate an account and $0.08 per page to send faxes. How many pages can she fax and stay within her budget? Identify a variable, then set up and solve an inequality. Interpret your solution. p = pages she can fax 25+ .08p ≤115 −25 −25 .08p ≤ 90 .08 .08 p ≤1125 p | p ≤1125{ } Maggie can send up to 1125 faxes. Monday, September 30, 13
  • 26. EXAMPLE 2 Solve the inequality. 13−11d ≥ 79 Monday, September 30, 13
  • 27. EXAMPLE 2 Solve the inequality. 13−11d ≥ 79 −13 −13 Monday, September 30, 13
  • 28. EXAMPLE 2 Solve the inequality. 13−11d ≥ 79 −13 −13 −11d ≥ 66 Monday, September 30, 13
  • 29. EXAMPLE 2 Solve the inequality. 13−11d ≥ 79 −13 −13 −11d ≥ 66 −11 −11 Monday, September 30, 13
  • 30. EXAMPLE 2 Solve the inequality. 13−11d ≥ 79 −13 −13 −11d ≥ 66 −11 −11 d ≤ −6 Monday, September 30, 13
  • 31. EXAMPLE 2 Solve the inequality. 13−11d ≥ 79 −13 −13 −11d ≥ 66 −11 −11 d ≤ −6 d | d ≤ −6{ } Monday, September 30, 13
  • 32. EXAMPLE 3 Define a variable, write an inequality and solve the problem.Then check your solution. Four times a number increased by twelve is less than the difference of that number and three. Monday, September 30, 13
  • 33. EXAMPLE 3 Define a variable, write an inequality and solve the problem.Then check your solution. Four times a number increased by twelve is less than the difference of that number and three. n = the number Monday, September 30, 13
  • 34. EXAMPLE 3 Define a variable, write an inequality and solve the problem.Then check your solution. Four times a number increased by twelve is less than the difference of that number and three. n = the number 4n +12 < n − 3 Monday, September 30, 13
  • 35. EXAMPLE 3 Define a variable, write an inequality and solve the problem.Then check your solution. Four times a number increased by twelve is less than the difference of that number and three. n = the number 4n +12 < n − 3 −n −n Monday, September 30, 13
  • 36. EXAMPLE 3 Define a variable, write an inequality and solve the problem.Then check your solution. Four times a number increased by twelve is less than the difference of that number and three. n = the number 4n +12 < n − 3 −n −n 3n +12 < −3 Monday, September 30, 13
  • 37. EXAMPLE 3 Define a variable, write an inequality and solve the problem.Then check your solution. Four times a number increased by twelve is less than the difference of that number and three. n = the number 4n +12 < n − 3 −n −n 3n +12 < −3 −12 −12 Monday, September 30, 13
  • 38. EXAMPLE 3 Define a variable, write an inequality and solve the problem.Then check your solution. Four times a number increased by twelve is less than the difference of that number and three. n = the number 4n +12 < n − 3 −n −n 3n +12 < −3 −12 −12 3n < −15 Monday, September 30, 13
  • 39. EXAMPLE 3 Define a variable, write an inequality and solve the problem.Then check your solution. Four times a number increased by twelve is less than the difference of that number and three. n = the number 4n +12 < n − 3 −n −n 3n +12 < −3 −12 −12 3n < −15 3n < −15 Monday, September 30, 13
  • 40. EXAMPLE 3 Define a variable, write an inequality and solve the problem.Then check your solution. Four times a number increased by twelve is less than the difference of that number and three. n = the number 4n +12 < n − 3 −n −n 3n +12 < −3 −12 −12 3n < −15 3n < −15 3 3 Monday, September 30, 13
  • 41. EXAMPLE 3 Define a variable, write an inequality and solve the problem.Then check your solution. Four times a number increased by twelve is less than the difference of that number and three. n = the number 4n +12 < n − 3 −n −n 3n +12 < −3 −12 −12 3n < −15 3n < −15 3 3 n < −5 Monday, September 30, 13
  • 42. EXAMPLE 3 Define a variable, write an inequality and solve the problem.Then check your solution. Four times a number increased by twelve is less than the difference of that number and three. n = the number 4n +12 < n − 3 −n −n 3n +12 < −3 −12 −12 3n < −15 3n < −15 3 3 n < −5 n | n < −5{ } Monday, September 30, 13
  • 43. EXAMPLE 4 6c + 3(2 − c) > −2c +1a. Monday, September 30, 13
  • 44. EXAMPLE 4 6c + 3(2 − c) > −2c +1a. 6c + 6 − 3c > −2c +1 Monday, September 30, 13
  • 45. EXAMPLE 4 6c + 3(2 − c) > −2c +1a. 6c + 6 − 3c > −2c +1 3c + 6 > −2c +1 Monday, September 30, 13
  • 46. EXAMPLE 4 6c + 3(2 − c) > −2c +1a. 6c + 6 − 3c > −2c +1 3c + 6 > −2c +1 +2c +2c Monday, September 30, 13
  • 47. EXAMPLE 4 6c + 3(2 − c) > −2c +1a. 6c + 6 − 3c > −2c +1 3c + 6 > −2c +1 +2c +2c 5c + 6 > +1 Monday, September 30, 13
  • 48. EXAMPLE 4 6c + 3(2 − c) > −2c +1a. 6c + 6 − 3c > −2c +1 3c + 6 > −2c +1 +2c +2c 5c + 6 > +1 −6 −6 Monday, September 30, 13
  • 49. EXAMPLE 4 6c + 3(2 − c) > −2c +1a. 6c + 6 − 3c > −2c +1 3c + 6 > −2c +1 +2c +2c 5c + 6 > +1 −6 −6 5c > −5 Monday, September 30, 13
  • 50. EXAMPLE 4 6c + 3(2 − c) > −2c +1a. 6c + 6 − 3c > −2c +1 3c + 6 > −2c +1 +2c +2c 5c + 6 > +1 −6 −6 5c > −5 5 5 Monday, September 30, 13
  • 51. EXAMPLE 4 6c + 3(2 − c) > −2c +1a. 6c + 6 − 3c > −2c +1 3c + 6 > −2c +1 +2c +2c 5c + 6 > +1 −6 −6 5c > −5 5 5 c > −1 Monday, September 30, 13
  • 52. EXAMPLE 4 6c + 3(2 − c) > −2c +1a. 6c + 6 − 3c > −2c +1 3c + 6 > −2c +1 +2c +2c 5c + 6 > +1 −6 −6 5c > −5 5 5 c > −1 c | c > −1{ } Monday, September 30, 13
  • 53. EXAMPLE 4 −7(k + 4)+11k ≥ 8k − 2(2k +1)b. Monday, September 30, 13
  • 54. EXAMPLE 4 −7(k + 4)+11k ≥ 8k − 2(2k +1)b. −7k − 28 +11k ≥ 8k − 4k −1 Monday, September 30, 13
  • 55. EXAMPLE 4 −7(k + 4)+11k ≥ 8k − 2(2k +1)b. −7k − 28 +11k ≥ 8k − 4k −1 4k − 28 ≥ 4k −1 Monday, September 30, 13
  • 56. EXAMPLE 4 −7(k + 4)+11k ≥ 8k − 2(2k +1)b. −7k − 28 +11k ≥ 8k − 4k −1 4k − 28 ≥ 4k −1 −4k −4k Monday, September 30, 13
  • 57. EXAMPLE 4 −7(k + 4)+11k ≥ 8k − 2(2k +1)b. −7k − 28 +11k ≥ 8k − 4k −1 4k − 28 ≥ 4k −1 −4k −4k −28 ≥ −1 Monday, September 30, 13
  • 58. EXAMPLE 4 −7(k + 4)+11k ≥ 8k − 2(2k +1)b. −7k − 28 +11k ≥ 8k − 4k −1 4k − 28 ≥ 4k −1 −4k −4k −28 ≥ −1 This is an untrue statement! Monday, September 30, 13
  • 59. EXAMPLE 4 −7(k + 4)+11k ≥ 8k − 2(2k +1)b. −7k − 28 +11k ≥ 8k − 4k −1 4k − 28 ≥ 4k −1 −4k −4k −28 ≥ −1 This is an untrue statement! ∅ Monday, September 30, 13
  • 60. EXAMPLE 4 2(4r + 3) ≤ 22 + 8(r − 2)c. Monday, September 30, 13
  • 61. EXAMPLE 4 2(4r + 3) ≤ 22 + 8(r − 2)c. 8r + 6 ≤ 22 + 8r −16 Monday, September 30, 13
  • 62. EXAMPLE 4 2(4r + 3) ≤ 22 + 8(r − 2)c. 8r + 6 ≤ 22 + 8r −16 8r + 6 ≤ 8r + 6 Monday, September 30, 13
  • 63. EXAMPLE 4 2(4r + 3) ≤ 22 + 8(r − 2)c. 8r + 6 ≤ 22 + 8r −16 8r + 6 ≤ 8r + 6 −8r −8r Monday, September 30, 13
  • 64. EXAMPLE 4 2(4r + 3) ≤ 22 + 8(r − 2)c. 8r + 6 ≤ 22 + 8r −16 8r + 6 ≤ 8r + 6 −8r −8r 6 ≤ 6 Monday, September 30, 13
  • 65. EXAMPLE 4 2(4r + 3) ≤ 22 + 8(r − 2)c. 8r + 6 ≤ 22 + 8r −16 8r + 6 ≤ 8r + 6 −8r −8r 6 ≤ 6 This is a true statement! Monday, September 30, 13
  • 66. EXAMPLE 4 2(4r + 3) ≤ 22 + 8(r − 2)c. 8r + 6 ≤ 22 + 8r −16 8r + 6 ≤ 8r + 6 −8r −8r 6 ≤ 6 This is a true statement! r | r is any real number{ } Monday, September 30, 13
  • 67. EXAMPLE 4 2(4r + 3) ≤ 22 + 8(r − 2)c. 8r + 6 ≤ 22 + 8r −16 8r + 6 ≤ 8r + 6 −8r −8r 6 ≤ 6 This is a true statement! r | r is any real number{ } or Monday, September 30, 13
  • 68. EXAMPLE 4 2(4r + 3) ≤ 22 + 8(r − 2)c. 8r + 6 ≤ 22 + 8r −16 8r + 6 ≤ 8r + 6 −8r −8r 6 ≤ 6 This is a true statement! r | r is any real number{ } r | r = { } or Monday, September 30, 13
  • 69. SUMMARIZER −3p + 7 > 2How could you solve without multiplying or dividing each side by a negative number. Monday, September 30, 13
  • 70. PROBLEM SETS Monday, September 30, 13
  • 71. PROBLEM SETS Problem Set 1: p. 298 #1-11 Problem Set 2: p. 298 #13-39 odd (skip #37), "The secret of success in life is for a man to be ready for his opportunity when it comes." - Earl of Beaconsfield Monday, September 30, 13