Name___________________________________________
Date_________________________
Algebra I – Pd ____
Inequalities & Sets (Chap. 3)
Review Sheet
Part I: Complete each question below. Answers go on the line to the left
of each number. Any work necessary is to go in your spiral notebooks.
_____ 1) Which number is in the solution set of 5 − 3𝑥 < 13 + 𝑥
(1) −6
(2) −4
(3) −2
(4) 0
_____ 2) Which of the following represents: “All numbers greater than positive six."
(1) (6, ∞)
(2) (6, ∞]
(3) [6, ∞)
(4) [6, ∞]
_____ 3) Which graph represents the inequality 𝑥 ≤ −3
(1)
(2)
(3)
(4)
_____ 4) Which verbal representation is represented in the accompanying graph
(1) 𝑥 is greater than −2
(2) 𝑥 is less than −2
(3) 𝑥 is greater than or equal to −2
(4) 𝑥 is less than or equal to −2
_____ 5) The additive inverse of −3 is
1
(1) 3
(2) 0
(3) 3
1
(4) − 3
_____ 6) What is the solution of 𝑥 − 12 > −18?
(1) 𝑥 < −30
(2) 𝑥 < −6
(3) 𝑥 > −6
(4) 𝑥 > −30
_____ 7) Which number is a solution of the inequality 7𝑥 − 5 ≥ −2
(1) −3
(2) −1
(3) 0
(4) 1
_____ 8) Which interval notation represents the set of all numbers from −3 through 5 inclusive?
(1) (−3, 5)
(2) (−3, 5]
(3) [−3, 5)
(4) [−3, 5]
_____ 9) All employees of a company work less than 35 hours. Which inequality describes
the situation?
(1) h < 35
(2) h ≤ 35
(3) h > 35
(4) h ≥ 35
Part II: Show all work in your spiral notebooks. No Work = No Credit!!
Basic Inequalities:
Section 1: Write an inequality that represents each verbal expression.
10) v is greater than 10.
11) 4 more than 𝑦 is less than −8
12) b is less than −3.
13) the product of 𝑥 and 5 is less than or equal to 15.
Section 2: Write each inequality in words.
14) 𝑛 < −4
15) 𝑚 ≥ 7
16) 𝑥 ≤ 6
17) 𝑦 > 1
Section 3: Determine if each number is a solution to the given inequality.
18) 2𝑚 − 4 ≥ 10
(a) −1
(b) 8
(c) 10
19) 4𝑥 + 3 > −9
(a) 0
(b) −2
(c) −4
Section 4: Solve and graph the following inequalities.
3
20) 41 − 4 𝑥 ≤ 53
21) 8(5𝑥 − 4) − 6(3𝑥 + 5) ≤ 4
22) 6(4𝑥 − 2) ≤ 5(7𝑥 + 2)
23) 5𝑥 − 9 ≤ 2𝑥 + 6
24) 3𝑥 + 2(8 − 𝑥) > 3
25) 4(7𝑥 + 3) − (16𝑥 − 13) < 97
Compound Inequalities:
Section 1: Write a compound inequality that represents each phrase. Graph the solution.
26) All real numbers that are greater than 3 or less than or equal to −5.
27) All real numbers that are between −7 and 4.
Section 2: Write a compound inequality that represents each graph.
28)
29)
Section 3: Solve and Graph each of the compound inequalities.
30) −2 < 3𝑥 + 4 < 13
31) 5𝑚 + 8 > 23
𝑜𝑟
7𝑚 < 7
1
(8𝑥 − 6) ≥ 5
32) 1 < 2𝑥 + 3 < 5
33) 156 < −3(12𝑥 − 4) ∩
34) −4𝑥 + 5 > 17 ∩ 2𝑥 − 4 > 6
35) 8(6𝑥 + 2) < −128 ∪ 5 − 6𝑥 ≤ −25
2
Sets:
Section 1: Given the following sets, determine if questions # 36 – 40 are true or false.
U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
A = {1, 3, 4, 5, 7, 8}
B = {2, 4, 6, 8}
C = {1, 3, 5, 7}
D = {1, 2, 3}
36) 𝐴 ∈ 𝑈
37) 𝐷 ∈ 𝐵
38) ∅ ∈ 𝐴
39) {1,2} ∈ 𝐷
40) 𝐵 ∈ 𝐴
Section 2: Given the following sets, write each set in roster form for questions # 41 – 48.
U = {a, b, c, d, e, f, g, h}
A = {a, b, c, d, e, f}
B = {a, c, e}
C = {a, f}
D = {d}
41) 𝐴′
42) 𝐴 ∩ 𝐵
43) 𝐶 𝑐
44) 𝐵 ∪ 𝐷
45) 𝐵′
46) 𝐴 ∪ 𝐷
47) 𝐵 ∩ 𝐶
̅
48) 𝐷
Answer Key
1) (4)
2) (1)
3) (4)
4) (2)
5) (3)
6) (3)
7) (4)
8) (4)
9) (1)
10) 𝒗 > 10
11) 𝒚 + 𝟒 < −8
12) 𝒃 < −3
14) n is less than – 𝟒
15) m is greater than or equal to 7
16) x is less than or equal to 𝟔
17) y is greater than 1
18) (a) No
19) (a) Yes
(b) Yes
(c)Yes
13) 𝟓𝒙 ≤ 𝟏𝟓
(b)Yes
(c)No
20) 𝒙 ≥ −𝟏𝟔
21) 𝒙 ≤ 𝟑
22) 𝒙 ≥ −𝟐
23) 𝒙 ≤ 𝟓
24) 𝒙 > −13
25) 𝒙 < 6
26) 𝒙 ≤ −𝟓 𝒐𝒓 𝒙 > 3
27) −𝟕 < 𝑥 < 4
28) −𝟐 ≤ 𝒙 < 7
29) 𝒙 ≤ −𝟑 𝒐𝒓 𝒙 > 1
30) −𝟐 < 𝑥 < 3
31) 𝒎 > 3 𝑜𝑟 𝑚 < 1
32) −𝟏 < 𝑥 < 1
33) no solution
34) no solution
35) 𝒙 < −3 ∪ 𝑥 ≥ 5
36) True
37) False
38) True
41) {𝒈, 𝒉}
42) {𝒂, 𝒄, 𝒆}
43) {𝒃, 𝒄, 𝒅, 𝒆, 𝒈, 𝒉}
45) {𝒃, 𝒅, 𝒇, 𝒈, 𝒉}
46) {𝒂, 𝒃, 𝒄, 𝒅, 𝒆, 𝒇}
39) True
47) {𝒂}
40) False
44) {𝒂, 𝒄, 𝒅, 𝒆}
48) {𝒂, 𝒃, 𝒄, 𝒆, 𝒇, 𝒈, 𝒉}