Download Algebra 1 Solving Inequalities Review

Name: ______________________
Class: _________________
Date: _________
Algebra 1 Solving Inequalities Review
What inequality represents the verbal expression?
1. all real numbers greater than or equal to 67
2. all real numbers less than 69
3. 8 less than a number n is less than 11
a. 11 – 8 < n
b. n – 8 < 11
c.
d.
8 – n < 11
11 < 8 – n
Which number is a solution of the inequality?
4. m >
a.
7
12
1
5. 6 ≥ 6k
a. 8
b.
–1
c.
–9
d.
–5
b.
18
c.
2
d.
1
What is the graph of the inequality?
6. d < 2
7. x ≥ –3
What inequality represents the graph?
8.
9.
What inequality describes the situation?
10. Let n = the number. A number exceeds 45.
What are the solutions of the inequality? Graph the solutions.
11. x − 3 ≤ − 12
12. y − 6 ≤ 2
13. r – 5 > 4
1
ID: A
Name: ______________________
ID: A
What are the solutions of the inequality? Graph the solutions.
14. x + 7 ≤ − 8
15. b + 8 ≤ 4
16. p + 4 > 1
17. Suppose you had d dollars in your bank account. You spent $12 but have at least $51 left. How much money
did you have initially? Write and solve an inequality that represents this situation.
18. Your class hopes to collect at least 325 cans of food for the annual food drive. There were 135 cans donated
the first week and 89 more the second week.
Write an inequality that describes this situation. Let c represent the number of cans of food that must be
collected by the end of the third week for your class to meet or surpass your goal. How many cans are needed
to meet or surpass your goal?
What are the solutions of the inequality? Graph the solutions.
19.
x
>9
9
20.
x
≥ −2
5
What are the solutions of the inequality? Graph and check the solutions.
21. −
x
≤2
4
1
22. − x ≤ 5
8
23. The French Club is sponsoring a bake sale. If their goal is to raise at least $140, how many pastries must they
sell at $3.50 each in order to meet that goal? Write and solve an inequality.
What are the solutions of the inequality? Graph the solutions.
24. −4x ≥ −12
25. –2m < –14
2
Name: ______________________
ID: A
What are the solutions of the inequality? Check the solutions.
26.
–
2
9
x–9<
5
10
27. 4x + 6 < –6
What are the solutions of the inequality?
28. 2(b – 8) > 12
29. q + 12 – 2(q – 22) > 0
What are the solutions of the inequality?
30. 12 + 10w ≥ 8(w + 12)
31. 12x – 3x + 11 > 4x – (17 – 9x)
32. 8n − 14 ≤ 13n + 6
What are the solutions of the inequality?
33. −5 ( 2x + 2 ) ≥ −10x − 17
a. x ≥ 7
b. x ≤ 19
c.
d.
all real numbers
no solution
34. 10x − 10 − 7x ≥ 3x − 2
a. x ≥ −8
b. x ≤ 8
c.
d.
all real numbers
no solution
How do you write the set in roster form? In set builder notation?
35. D is the set of whole numbers less than 3.
a. D = {0,1,2,3,4,5}; D = {x is a whole number, x < 3}
b. D = {0,1}; D = {x | x < 3}
c. D = {0,1,2}; D = {x | x is a whole number, x < 3}
d. D = {0,1,2,3,4,5,6,7}; D = {x < 3}
36. G is the set of odd natural numbers that are less than or equal to 1.
37. H is the set of even integers less than 6 but greater than or equal to 0.
3
Name: ______________________
ID: A
In set builder notation, how do you write the solutions of the inequality?
38. 3x + 10 ≥ 4
ÔÏ
Ô¸
a. ÌÔ x | x ≥ −2 ˝Ô
Ó
˛
ÔÏ
Ô¸
b. ÌÔ x | x ≤ 2 ˝Ô
Ó
˛
39. −2 − x ≥ −1
ÏÔ
¸Ô
a. ÔÌ x | x ≤ 1 Ô˝
Ó
˛
ÏÔ
¸Ô
b. ÔÌ x | x ≥ 1 Ô˝
Ó
˛
c.
d.
c.
d.
ÔÏ
Ô¸
ÌÔ x | x ≤ −2 ˝Ô
Ó
˛
ÔÏ
Ô¸
ÌÔ x | x ≥ 2 ˝Ô
Ó
˛
ÏÔ
¸Ô
ÔÌÓ x | x ≥ −1 Ô˝˛
ÏÔ
¸Ô
ÔÌÓ x | x ≤ −1 Ô˝˛
What are all the subsets of the set?
40. {–1, 9}
a. ∅, {−1}, {9}
b. {−1}, {9}, {−1, 9}
c.
d.
∅, {−1}, {9}, {−1, 9}
{−1}, {9}
41. Suppose U = {–10, –6, –2, 0, 3, 5} is the universal set and T is the set {–10, –6, 0}. What is the complement
of set T?
a. {–2, 3, 5}
c. {–6, –2, 0, 3, 5}
b. {–10, –6, 0}
d. {0, 3, 5}
42. Suppose U = {–4, 3, 4, 5, 9, 10} is the universal set and T is the set {–4, 3, 5}. What is the complement of set
T?
a. {–4, 3, 5}
c. {4, 9, 10}
b. {5, 9, 10}
d. {3, 4, 5, 9, 10}
What compound inequality represents the phrase? Graph the solutions.
43. all real numbers that are greater than –8 and less than 8
44. all real numbers w that are less than –7 or greater than 14
45. all real numbers at least –5 and at most 9
46. all real numbers at most –8.5 or at least 6.5
What are the solutions of the compound inequality? Graph the solutions.
47. −2 ≤ 2x − 4 < 8
48. –2 < 4x – 10 < 6
4
Name: ______________________
ID: A
What are the solutions of the compound inequality? Graph the solutions.
49. 2x – 2 < –12 or 2x + 3 > 7
50.
2x − 1
+ 3 ≤ −4
3
or
8x − 2
−1≥ 6
2
51. What is the graph of (–8, 2]?
a.
b.
c.
d.
52. How do you write x ≥ −6 and x < −3 in interval notation?
a.
b.
[–6, –3]
(–6, –3)
c.
d.
[–6, –3)
(–6, –3]
53. What is the graph of (−∞, −8) or (6, ∞)?
a.
b.
c.
d.
54. How do you write (−∞, 8) or (10, ∞) as an inequality?
a.
b.
x < 8 or x > 10
x < 10 or x > 8
c.
d.
x < 8 and x > 10
x < 10 and x > 8
5
Name: ______________________
ID: A
Let X = {x | x is a whole number less than 15}, Y = { x | x is a multiple of 3}, Z = {x | x is a real
number greater than or equal to 5.5}.
55. What is X ∩ Y?
56. What is X ∩ Z?
57. A doctor is examining 3 patients. Which symptoms do all three patients have in common?
58. Of 410 consumers polled, some purchase music on CDs, some only download music, and some do both. If 290
people polled purchase CDs and 220 purchase CDs and download music, how many people download music?
59. Of 480 consumers polled, some purchase ice cream, some purchase frozen yogurt, and some purchase both. If
260 people polled purchase ice cream and 200 purchase both ice cream and frozen yogurt, how many people
purchase frozen yogurt?
CUMULATIVE REVIEW SEÇTION
2
60. 5 ( 14 − 2 ) ÷ 2
ÍÈÍ 2 Ê 2
˙˘˙
2ˆ
61. 13 ÍÍÍ 6 ÷ ÁÁÁÁ 5 − 4 ˜˜˜˜ + 9 ˙˙˙
ÍÎ
˙˚
Ë

62. Evaluate u + xy, for u = 18, x = 10, and y = 8.
6
Name: ______________________
63. Evaluate
ID: A
u
2
+ xy , for u = 20, x = 4, y = 7, and z = 10.
z
64. To which subsets of the real numbers does the number 22 belong?
65. To which subsets of the real numbers does the number
42 belong?
What is each difference?
66.
9 1
−
4 7
What is each product?
67.
5 10
•
10 3
What is the simplified form of each expression?
68.
1
(21m + 27)
3
What is the solution of the equation?
69. 3(y – 5) + 2 = 5
70. 2.4x + 2.6 = 17
What is the solution of the equation?
71. 6x – 3 = 5x – 5
72. –4x – 9 = –5 – 6x
What is the solution of the equation?
73. 5 ( 10x − 10 ) = −5 ( −4x + 4 )
What is the solution of each equation?
74. 2(h − 8) − h = h − 16
a. 8
b. −8
c.
d.
infinitely many solutions
no solution
7
Name: ______________________
75. 3 + 6z = 13 + 6z
5
a. −
6
2
b. 2
3
ID: A
c.
infinitely many solutions
d.
no solution
What is the given amount converted to the given units?
76. 195 s; minutes
77. A car is driving at a speed of 45 mi/h. What is the speed of the car in feet per minute?
What is the solution of the proportion?
78.
h
19
=
−8
−2
a. 76
b. –152
c.
d.
–38
16
8
ID: A
Algebra 1 Solving Inequalities Review
Answer Section
1.
2.
3.
4.
5.
x ≥ 67
x < 69
B
A
D
6.
7.
8. x > –8
1
2
10. n > 45
11. x ≤ − 9
9. m ≥ −
12. y ≤ 8
13. r > 9
14. x ≤ − 15
15. b ≤ − 4
16. p > –3
17. d − 12 ≥ 51; d ≥ 63
18. 135 + 89 + c ≥ 325; c ≥ 101
19. x > 81
20. x ≥ − 10
1
ID: A
21. x ≥ − 8
22. x ≥ −40
23. 3.50p ≥ 140; p ≥ 40
24. x ≤ 3
25. m > 7
26. x > −24
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
40.
41.
42.
43.
3
4
x < –3
b > 14
q < 56
w ≥ 42
x<7
n ≥ –4
C
D
C
G = {1}; G = {x | x is an odd natural number, x ≤ 1}
ÔÏ
Ô¸
H = ÌÔ 0, 2, 4 ˝Ô ; H = {x | x is an even integer, x < 6, x ≥ 0}
Ó
˛
A
D
C
A
C
–8 < x < 8
44. w < –7 or w > 14
45. −5 ≤ x ≤ 9
46. b ≤ − 8.5 or b ≥ 6.5
2
ID: A
47. 1 ≤ x < 6
48. 2 < x < 4
49. x < –5 or x > 2
50. x ≤ − 10 or x ≥ 2
51.
52.
53.
54.
55.
56.
57.
58.
59.
60.
61.
62.
63.
64.
65.
66.
67.
68.
69.
70.
71.
72.
73.
74.
75.
76.
77.
78.
C
C
C
A
{0, 3, 6, 9, 12}
{6, 7, 8, 9, 10, 11, 12, 13, 14}
{fever, joint pain, tiredness}
340
420
360
169
98
198
integers, rational numbers
irrational numbers
59
28
5
3
7m + 9
6
6
–2
2
1
C
D
3.25 min
3,960 ft/min
A
3