1. 5.3 – Solving Multi-Step Inequalities

2. *Just like solving equations*

3. *Just like solving equations* Example 1

4. *Just like solving equations* Example 1 - Solve 7x – 5 > 6x – 4 and graph on a number line.

5. *Just like solving equations* Example 1 - Solve 7x – 5 > 6x – 4 and graph on a number line. 7x – 5 > 6x – 4

6. *Just like solving equations* Example 1 - Solve 7x – 5 > 6x – 4 and graph on a number line. 7x – 5 > 6x – 4 -6x -6x

7. *Just like solving equations* Example 1 - Solve 7x – 5 > 6x – 4 and graph on a number line. 7x – 5 > 6x – 4 -6x -6x x – 5

8. *Just like solving equations* Example 1 - Solve 7x – 5 > 6x – 4 and graph on a number line. 7x – 5 > 6x – 4 -6x -6x x – 5 > -4

9. *Just like solving equations* Example 1 - Solve 7x – 5 > 6x – 4 and graph on a number line. 7x – 5 > 6x – 4 -6x -6x x – 5 > -4 +5 +5

10. *Just like solving equations* Example 1 - Solve 7x – 5 > 6x – 4 and graph on a number line. 7x – 5 > 6x – 4 -6x -6x x – 5 > -4 +5 +5 x

11. *Just like solving equations* Example 1 - Solve 7x – 5 > 6x – 4 and graph on a number line. 7x – 5 > 6x – 4 -6x -6x x – 5 > -4 +5 +5 x >

12. *Just like solving equations* Example 1 - Solve 7x – 5 > 6x – 4 and graph on a number line. 7x – 5 > 6x – 4 -6x -6x x – 5 > -4 +5 +5 x > 1

13. *Just like solving equations* Example 1 - Solve 7x – 5 > 6x – 4 and graph on a number line. 7x – 5 > 6x – 4 -6x -6x x – 5 > -4 +5 +5 x > 1

14. *Just like solving equations* Example 1 - Solve 7x – 5 > 6x – 4 and graph on a number line. 7x – 5 > 6x – 4 -6x -6x x – 5 > -4 +5 +5 x > 1 0

15. *Just like solving equations* Example 1 - Solve 7x – 5 > 6x – 4 and graph on a number line. 7x – 5 > 6x – 4 -6x -6x x – 5 > -4 +5 +5 x > 1 0 1

16. *Just like solving equations* Example 1 - Solve 7x – 5 > 6x – 4 and graph on a number line. 7x – 5 > 6x – 4 -6x -6x x – 5 > -4 +5 +5 x > 1 0 1

17. *Just like solving equations* Example 1 - Solve 7x – 5 > 6x – 4 and graph on a number line. 7x – 5 > 6x – 4 -6x -6x x – 5 > -4 +5 +5 x > 1 0 1

18. Example 2

19. Example 2 – Solve –m < -m + 4 and graph. 9

20. Example 2 – Solve –m < -m + 4 and graph. 9 –m < -m + 4 9

21. Example 2 – Solve –m < -m + 4 and graph. 9 –m < -m + 4 9 9·–m < -m + 4 ·9 9

22. Example 2 – Solve –m < -m + 4 and graph. 9 –m < -m + 4 9 9·–m < -m + 4 ·9 9

23. Example 2 – Solve –m < -m + 4 and graph. 9 –m < -m + 4 9 9·–m < -m + 4 ·9 9

24. Example 2 – Solve –m < -m + 4 and graph. 9 –m < -m + 4 9 9·–m < -m + 4 ·9 9 –9m

25. Example 2 – Solve –m < -m + 4 and graph. 9 –m < -m + 4 9 9·–m < -m + 4 ·9 9 –9m <

26. Example 2 – Solve –m < -m + 4 and graph. 9 –m < -m + 4 9 9·–m < -m + 4 ·9 9 –9m < -m + 4

27. Example 2 – Solve –m < -m + 4 and graph. 9 –m < -m + 4 9 9·–m < -m + 4 ·9 9 –9m < -m + 4 +m

28. Example 2 – Solve –m < -m + 4 and graph. 9 –m < -m + 4 9 9·–m < -m + 4 ·9 9 –9m < -m + 4 +m –8m

29. Example 2 – Solve –m < -m + 4 and graph. 9 –m < -m + 4 9 9·–m < -m + 4 ·9 9 –9m < -m + 4 +m –8m <

30. Example 2 – Solve –m < -m + 4 and graph. 9 –m < -m + 4 9 9·–m < -m + 4 ·9 9 –9m < -m + 4 +m –8m < 4

31. Example 2 – Solve –m < -m + 4 and graph. 9 –m < -m + 4 9 9·–m < -m + 4 ·9 9 –9m < -m + 4 +m –8m < 4 -8 -8

32. Example 2 – Solve –m < -m + 4 and graph. 9 –m < -m + 4 9 9·–m < -m + 4 ·9 9 –9m < -m + 4 +m –8m < 4 -8 -8 m

33. Example 2 – Solve –m < -m + 4 and graph. 9 –m < -m + 4 9 9·–m < -m + 4 ·9 9 –9m < -m + 4 +m –8m < 4 -8 -8 m >

34. Example 2 – Solve –m < -m + 4 and graph. 9 –m < -m + 4 9 9·–m < -m + 4 ·9 9 –9m < -m + 4 +m –8m < 4 -8 -8 m >

35. Example 2 – Solve –m < -m + 4 and graph. 9 –m < -m + 4 9 9·–m < -m + 4 ·9 9 –9m < -m + 4 +m –8m < 4 -8 -8 m > -½

36. Example 2 – Solve –m < -m + 4 and graph. 9 –m < -m + 4 9 9·–m < -m + 4 ·9 9 –9m < -m + 4 +m –8m < 4 -8 -8 m > -½

37. Example 2 – Solve –m < -m + 4 and graph. 9 –m < -m + 4 9 9·–m < -m + 4 ·9 9 –9m < -m + 4 +m –8m < 4 -8 -8 m > -½ 0

38. Example 2 – Solve –m < -m + 4 and graph. 9 –m < -m + 4 9 9·–m < -m + 4 ·9 9 –9m < -m + 4 +m –8m < 4 -8 -8 m > -½ 0 -1½-½

39. Example 2 – Solve –m < -m + 4 and graph. 9 –m < -m + 4 9 9·–m < -m + 4 ·9 9 –9m < -m + 4 +m –8m < 4 -8 -8 m > -½ 0 -1½-½

40. Example 3

41. Example 3 – Define a variable and write an inequality for each problem. Then solve.

42. The product of –4 and a number is at least 35.

43. Example 3 – Define a variable and write an inequality for each problem. Then solve. The product of –4 and a number is at least 35.

44. Example 3 – Define a variable and write an inequality for each problem. Then solve. The product of –4 and a number is at least 35. -4x

45. Example 3 – Define a variable and write an inequality for each problem. Then solve. The product of –4 and a number is at least 35. -4x

46. Example 3 – Define a variable and write an inequality for each problem. Then solve. The product of –4 and a number is at least 35. -4x >

47. Example 3 – Define a variable and write an inequality for each problem. Then solve. The product of –4 and a number is at least 35. -4x >

48. Example 3 – Define a variable and write an inequality for each problem. Then solve. The product of –4 and a number is at least 35. -4x > 35

49. Example 3 – Define a variable and write an inequality for each problem. Then solve. The product of –4 and a number is at least 35. -4x > 35 -4 -4

50. Example 3 – Define a variable and write an inequality for each problem. Then solve. The product of –4 and a number is at least 35. -4x > 35 -4 -4 x <

51. Example 3 – Define a variable and write an inequality for each problem. Then solve. The product of –4 and a number is at least 35. -4x > 35 -4 -4 x < -8.75

52. Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80?

54. 75%( )

55. Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80? 75%( )

56. Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80? 75%( ? )

57. Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80? 75%( ? )

58. Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80? 75%( ? ) +

59. Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80? 75%( ? ) +

60. Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80? 75%( ? ) + 25%( )

61. Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80? 75%( ? ) + 25%( )

62. Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80? 75%( ? ) + 25%( ? )

63. Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80? 75%( ? ) + 25%( ? )

64. Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80? 75%(76) + 25%( ? )

65. Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80? 75%(76) + 25%( ? )

66. Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80? 75%(76) + 25%(x)

67. Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80? 75%(76) + 25%(x) ≥ 80

68. Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80? 75%(76) + 25%(x) ≥ 80

69. Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80? 75%(76) + 25%(x) ≥ 80 0.75

70. Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80? 75%(76) + 25%(x) ≥ 80 0.75(76)

71. Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80? 75%(76) + 25%(x) ≥ 80 0.75(76) +

72. Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80? 75%(76) + 25%(x) ≥ 80 0.75(76) + 0.25

73. Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80? 75%(76) + 25%(x) ≥ 80 0.75(76) + 0.25(x)

74. Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80? 75%(76) + 25%(x) ≥ 80 0.75(76) + 0.25(x) ≥ 80

75. Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80? 75%(76) + 25%(x) ≥ 80 0.75(76) + 0.25(x) ≥ 80 57

76. Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80? 75%(76) + 25%(x) ≥ 80 0.75(76) + 0.25(x) ≥ 80 57 + 0.25x

77. Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80? 75%(76) + 25%(x) ≥ 80 0.75(76) + 0.25(x) ≥ 80 57 + 0.25x ≥ 80

78. Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80? 75%(76) + 25%(x) ≥ 80 0.75(76) + 0.25(x) ≥ 80 57 + 0.25x ≥ 80 -57 -57

79. Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80? 75%(76) + 25%(x) ≥ 80 0.75(76) + 0.25(x) ≥ 80 57 + 0.25x ≥ 80 -57 -57 0.25x

80. Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80? 75%(76) + 25%(x) ≥ 80 0.75(76) + 0.25(x) ≥ 80 57 + 0.25x ≥ 80 -57 -57 0.25x ≥ 23

81. Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80? 75%(76) + 25%(x) ≥ 80 0.75(76) + 0.25(x) ≥ 80 57 + 0.25x ≥ 80 -57 -57 0.25x ≥ 23 0.25 0.25

82. Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80? 75%(76) + 25%(x) ≥ 80 0.75(76) + 0.25(x) ≥ 80 57 + 0.25x ≥ 80 -57 -57 0.25x ≥ 23 0.25 0.25 x

83. Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80? 75%(76) + 25%(x) ≥ 80 0.75(76) + 0.25(x) ≥ 80 57 + 0.25x ≥ 80 -57 -57 0.25x ≥ 23 0.25 0.25 x ≥

84. Ex. 4 The final grade for a class is calculated by taking 75% of the average test score and adding 25% of the score on the final exam. If all scores are out of 100 and a student has a 76 test average, what score does the student need to make on the final exam to have a final grade of at least 80? 75%(76) + 25%(x) ≥ 80 0.75(76) + 0.25(x) ≥ 80 57 + 0.25x ≥ 80 -57 -57 0.25x ≥ 23 0.25 0.25 x ≥ 92