Solve each inequality. Graph and check your solutions.

33. x + 5 ≤ 10 x plus 5 less than or equal to 10
34. n + 6 > − 2 n plus 6 greater than negative 2
35. 2 < 9 + c 2 less than 9 plus c
36. − 1 ≥ 5 + b negative 1 greater than or equal to 5 plus b
37. 1 4 + a ≥ − 3 4 1 fourth , plus eh greater than or equal to negative , 3 fourths
38. 8.6 + z < 14 8.6 plus z less than 14
39. 1 3 < n + 3 1 third , less than n plus 3
40. 3.8 ≥ b + 4 3.8 greater than or equal to b plus 4
41. 3 5 + d ≥ − 2 5 3 fifths , plus d greater than or equal to negative , 2 fifths

    See Problem 4.

42. Exercise Your goal is to take at least 10,000 steps per day. According to your pedometer, you have walked 5274 steps. Write and solve an inequality to find the possible numbers of steps you can take to reach your goal.
43. Fundraising The environmental club is selling indoor herb gardens for Earth Day. Each member is encouraged to sell at least 10 gardens. You sell 3 gardens on Monday and 4 gardens on Tuesday. Write and solve an inequality to find the possible numbers of gardens you can sell to reach your goal.
44. Monthly Budget You earn $250 per month from your part-time job. You are in a kayaking club that costs $20 per month, and you save at least $100 each month. Write and solve an inequality to find the possible amounts you have left to spend each month.

B Apply

Tell what you can do to the first inequality in order to get the second.

45. 36 ≤ − 4 + y ; 40 ≤ y 36 less than or equal to negative 4 plus y semicolon 40 less than or equal to y
46. 9 + b > 24 ; b > 15 9 plus b greater than 24 semicolon b greater than 15
47. m − 1 2 < 3 8 ; m < 7 8 m minus , 1 half , less than , 3 eighths , semicolon m less than , 7 eighths

Tell whether the two inequalities in each pair are equivalent.

48. 45 ≤ − 5 + z ; 40 ≤ z 45 less than or equal to negative 5 plus z semicolon 40 less than or equal to z
49. 7 + c > 33 ; c > 26 7 plus c greater than 33 semicolon c greater than 26
50. n − 1 4 < 5 4 ; n < 1 n minus , 1 fourth , less than , 5 fourths , semicolon n less than 1

You can draw a model to represent an inequality. For example, the model below represents the inequality 85 + v < 120 . 85 plus bold italic v less than 120 .  Draw a model to represent each inequality below.

51. 17 + x < 51 17 plus x less than 51
52. 12 + y > 18 12 plus y greater than 18
53. − 3 + m ≤ 13 negative 3 plus m less than or equal to 13

Solve each inequality. Justify each step.

54. y − 4 + 2 ≥ 10 y minus 4 plus 2 greater than or equal to 10
55. 3 5 + d ≤ 2 3 5 3 fifths , plus d less than or equal to 2 , and 3 fifths
56. z − 1.4 < 3.9 z minus 1.4 less than 3.9
57. − 5 > p − 1 5 negative 5 greater than p minus , 1 fifth
58. a + 5.2 < − 4.6 eh plus 5.2 less than negative 4.6
59. − 3.1 > z − 1.9 negative 3.1 greater than z minus 1.9
60. 5 8 + v − 7 16 > 0 5 eighths , plus v minus , 7 sixteenths , greater than 0
61. − 4 p − 2 + 5 p > 10 negative 4 p minus 2 plus 5 p greater than 10
62. 5 y + 5 − 4 y < 8 5 y plus 5 minus 4 y less than 8
63. h − 1 8 ≥ − 1 h minus , 1 eighth , greater than or equal to negative 1
64. 8 v − 7 v − 3 ≥ − 6 8 v minus 7 v minus 3 greater than or equal to negative 6
65. 5 ≥ m − 7 16 5 greater than or equal to m minus , 7 sixteenths
66. Government The U.S. Senate is composed of 2 senators from each of the 50 states. In order for a treaty to be ratified, at least two thirds of the senators present must approve the treaty. Suppose all senators are present and 48 of them have voted in favor of a treaty. What are the possible numbers of additional senators who must vote in favor of the treaty in order to ratify it?

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