Name: ________________________ Class: ___________________ Date: __________
Inequalities Study Guide
Multiple Choice
Identify the choice that best completes the statement or answers the question.
Which number is a solution of the inequality?
____
15
8
a. I don’t know.
b. 0
c. –9
1. m >
d.
e.
3
–11
Write the inequality in words.
____
2. 3n < 52
a. fifty-two less than three times n
b. Three times n is less than fifty-two.
c. Three times n is less than or equal to fifty-two.
d. Three times n is greater than fifty-two.
e. I don’t know.
____
3. 5n – 10 > 26
a. Five times n less than ten is twenty-six.
b. Ten plus five times a number is less than or equal to twenty-six.
c. Ten less than five times a number is greater than twenty-six.
d. Ten less than a number is less than or equal to twenty-six.
e. I don’t know.
Graph the inequality.
____
4. p < 3
a.
b.
d.
I don’t know.
e.
c.
1
ID: A
Name: ________________________
____
5. a > −
ID: A
9
2
a.
d.
b.
e.
I don’t know.
c.
____
6. -3 ≥ x
a.
d.
b.
e.
I don’t know.
c.
Write an inequality for the graph.
____
7.
a.
b.
c.
____
I don’t know.
x<3
x>3
d.
e.
x≤3
x < –3
8. Tina can type at least 40 words per minute. Write and graph an inequality to model this situation.
a. I don’t know.
d. t ≤ 40
b.
t > 40
c.
t < 40
e.
t ≥ 40
d.
e.
t ≥ 66
I don’t know.
Write an inequality to model the situation.
____
9. Thomas earned $66 or more.
a. t > 66
b. t ≤ 66
c. t < 66
2
Name: ________________________
____ 10. A number exceeds 48.
a. I don’t know.
b. n > 48
c. n ≤ 48
ID: A
d.
e.
n ≥ 48
n < 48
Solve the inequality. Then graph your solution.
____ 11. x − 1 ≤ − 5
I don’t know.
d.
x≤
b.
x ≤ −4
e.
x≤6
c.
x ≤ −6
d.
y ≤ −45
e.
y³−
x
≥ −6
3
a. x ≥ − 18
d.
I don’t know.
b.
x≥9
e.
x ≤ − 18
c.
x ≥ −9
1
____ 12. − y ≤ 5
9
a. y ≥ −45
____ 13.
−5
1
a.
1
9
b.
y≤5
c.
I don’t know.
3
5
9
Name: ________________________
____ 14. 3x ≥ −12
a. x ≤ − 4
ID: A
d.
x ≥ −4
e.
x ≥ 15
d.
q>3
e.
q > –10
____ 16. −4 ≤ 2x − 4 < 2
a. 2 ≤ x < 5
d.
−2 ≤ x < − 4
b.
0≤ x < −1
e.
0≤x< 3
c.
I don’t know.
d.
–16 < x < 6
e.
–20 < x < 2
b.
x > − 15
c.
I don’t know.
____ 15. –5q < –15
a. q < 3
b.
q < –10
c.
I don’t know.
____ 17. –16 < 2x – 2 < 6
a. I don’t know.
b.
–7 < x < 4
c.
−9 < x < 2
4
Name: ________________________
____ 18.
ID: A
| d + 2| ≥ 6
a. d ≤ − 4 or d ≥ 4
d.
d ≤ − 8 or d ≥ 4
b.
d ≥ − 8 or d ≥ 4
e.
I don’t know.
c.
d ≤ − 8 or d ≥ 4
d.
–13 < x < 3
e.
–28 < x < 4
____ 19. | 2x + 10 | < 16
a. –13 > x > 3
b.
–3 < x < 3
c.
I don’t know.
____ 20. The French club is sponsoring a bake sale. If their goal is to raise at least $ 110, how many pastries must they
sell at $2.50 each in order to meet that goal? Write and solve an inequality.
a. 2.50p ≥ 110; p ≥ 44
d. I don’t know.
b. 2.50p ≥ 110; p ≥ 275
e. 110p ≥ 2.50; p ≥ 44
c. 2.50p ≥ 110; p ≥ 107.5
Write a compound inequality that the graph could represent.
____ 21.
a.
b.
c.
−2 ≤ x < 4
−4 < x ≤ 2
x ≥ −4 or x < 2
d.
e.
−4 ≤ x < 2
I don’t know.
a.
b.
c.
I don’t know.
r > − 5 or r ≤ 2
−2 ≤ r < 5
d.
e.
r < − 2 or r ≥ 5
r < − 5 or r ≥ 2
____ 22.
5
Name: ________________________
ID: A
____ 23. A student scored 78 and 97 on her first two quizzes. Write and solve a compound inequality to find the
possible values for a third quiz score that would give her an average between 80 and 90, inclusive.
a. I don’t know.
78 + 97
+ n ≤ 90; − 7.5 ≤ n ≤ 2.5
b. 80 ≤
2
78 + 97 + n
≤ 90; 65 ≤ n ≤ 95
c. 80 ≤
3
78 + 97 + n
≤ 80; 95 ≤ n ≤ 65
d. 90 ≤
3
80 + 97 + n
≤ 90; 57 ≤ n ≤ 93
e. 78 ≤
3
Solve the compound inequality. Graph your solution.
____ 24. 2x – 8 < –10 or 4x + 2 > 14
a. x < –1 or x > 3
b.
x < –1 or x > 4
c.
x < −9 or x > 4
d.
x < –4 or x > 8
e.
I don’t know.
Other
25. Are the solutions of the compound inequality x < 3 OR x > 6 different from the solutions to the compound
inequality x < 3 AND x > 6 ? Explain.
6
ID: A
Inequalities Study Guide
Answer Section
MULTIPLE CHOICE
1. ANS:
OBJ:
STA:
KEY:
2. ANS:
OBJ:
STA:
3. ANS:
OBJ:
STA:
4. ANS:
OBJ:
STA:
KEY:
5. ANS:
OBJ:
STA:
KEY:
6. ANS:
OBJ:
STA:
KEY:
7. ANS:
OBJ:
STA:
KEY:
8. ANS:
OBJ:
STA:
KEY:
9. ANS:
OBJ:
STA:
KEY:
10. ANS:
OBJ:
STA:
D
PTS: 1
DIF: L2
REF: 4-1 Inequalities and Their Graphs
4-1.1 Identifying Solutions of Inequalities
NAT: NAEP 2005 A3a | ADP J.3.1
8NJ 4.5.E.1d
TOP: 4-1 Example 1
solution of the inequality | inequality
B
PTS: 1
DIF: L3
REF: 4-1 Inequalities and Their Graphs
4-1.2 Graphing and Writing Inequalities in One Variable NAT: NAEP 2005 A3a | ADP J.3.1
8NJ 4.5.E.1d
KEY: translating an inequality | inequality
C
PTS: 1
DIF: L3
REF: 4-1 Inequalities and Their Graphs
4-1.2 Graphing and Writing Inequalities in One Variable NAT: NAEP 2005 A3a | ADP J.3.1
8NJ 4.5.E.1d
KEY: translating an inequality | inequality
C
PTS: 1
DIF: L2
REF: 4-1 Inequalities and Their Graphs
4-1.2 Graphing and Writing Inequalities in One Variable NAT: NAEP 2005 A3a | ADP J.3.1
8NJ 4.5.E.1d
TOP: 4-1 Example 3
graphing | inequality
C
PTS: 1
DIF: L2
REF: 4-1 Inequalities and Their Graphs
4-1.2 Graphing and Writing Inequalities in One Variable NAT: NAEP 2005 A3a | ADP J.3.1
8NJ 4.5.E.1d
TOP: 4-1 Example 3
graphing | inequality
E
PTS: 1
DIF: L2
REF: 4-1 Inequalities and Their Graphs
4-1.2 Graphing and Writing Inequalities in One Variable NAT: NAEP 2005 A3a | ADP J.3.1
8NJ 4.5.E.1d
TOP: 4-1 Example 3
graphing | inequality
B
PTS: 1
DIF: L2
REF: 4-1 Inequalities and Their Graphs
4-1.2 Graphing and Writing Inequalities in One Variable NAT: NAEP 2005 A3a | ADP J.3.1
8NJ 4.5.E.1d
TOP: 4-1 Example 4
writing an inequality from a graph | graphing
E
PTS: 1
DIF: L3
REF: 4-1 Inequalities and Their Graphs
4-1.2 Graphing and Writing Inequalities in One Variable NAT: NAEP 2005 A3a | ADP J.3.1
8NJ 4.5.E.1d
TOP: 4-1 Example 5
translating an inequality | word problem | problem solving
D
PTS: 1
DIF: L3
REF: 4-1 Inequalities and Their Graphs
4-1.2 Graphing and Writing Inequalities in One Variable NAT: NAEP 2005 A3a | ADP J.3.1
8NJ 4.5.E.1d
TOP: 4-1 Example 5
modeling with inequalities | translating an inequality
B
PTS: 1
DIF: L2
REF: 4-1 Inequalities and Their Graphs
4-1.2 Graphing and Writing Inequalities in One Variable NAT: NAEP 2005 A3a | ADP J.3.1
8NJ 4.5.E.1d
KEY: modeling with inequalities | translating an inequality
1
ID: A
11. ANS:
REF:
OBJ:
NAT:
STA:
KEY:
12. ANS:
REF:
OBJ:
NAT:
STA:
TOP:
KEY:
13. ANS:
REF:
OBJ:
NAT:
STA:
TOP:
KEY:
14. ANS:
REF:
OBJ:
NAT:
STA:
TOP:
15. ANS:
REF:
OBJ:
NAT:
STA:
TOP:
KEY:
16. ANS:
OBJ:
NAT:
TOP:
KEY:
17. ANS:
OBJ:
NAT:
TOP:
KEY:
18. ANS:
REF:
OBJ:
NAT:
STA:
KEY:
B
PTS: 1
DIF: L2
4-2 Solving Inequalities Using Addition and Subtraction
4-2.1 Using Addition to Solve Inequalities
NAEP 2005 N5e | NAEP 2005 A4a | NAEP 2005 A4c | ADP J.3.1
8NJ 4.5.D.4 | NJ 4.3.12 D.2a | 8NJ 4.5.E.1d
TOP: 4-2 Example 1
Addition Property of Inequality | solving inequalities | graphing
A
PTS: 1
DIF: L3
4-3 Solving Inequalities Using Multiplication and Division
4-3.1 Using Multiplication to Solve Inequalities
NAEP 2005 A4a | NAEP 2005 A4c | ADP J.3.1
NJ 4.3.12 D.2a | 8NJ 4.5.D.4 | 8NJ 4.5.E.1d | NJ 4.3.12 D.2a
4-3 Example 2
Multiplication Property of Inequality for c < 0 | solving inequalities
A
PTS: 1
DIF: L2
4-3 Solving Inequalities Using Multiplication and Division
4-3.1 Using Multiplication to Solve Inequalities
NAEP 2005 A4a | NAEP 2005 A4c | ADP J.3.1
NJ 4.3.12 D.2a | 8NJ 4.5.D.4 | 8NJ 4.5.E.1d | NJ 4.3.12 D.2a
4-3 Example 1
Multiplication Property of Inequality for c > 0 | solving inequalities
D
PTS: 1
DIF: L2
4-3 Solving Inequalities Using Multiplication and Division
4-3.2 Using Division to Solve Inequalities
NAEP 2005 A4a | NAEP 2005 A4c | ADP J.3.1
NJ 4.3.12 D.2a | 8NJ 4.5.D.4 | 8NJ 4.5.E.1d | NJ 4.3.12 D.2a
4-3 Example 3
KEY: Division Property of Inequality | solving inequalities
D
PTS: 1
DIF: L2
4-3 Solving Inequalities Using Multiplication and Division
4-3.2 Using Division to Solve Inequalities
NAEP 2005 A4a | NAEP 2005 A4c | ADP J.3.1
NJ 4.3.12 D.2a | 8NJ 4.5.D.4 | 8NJ 4.5.E.1d | NJ 4.3.12 D.2a
4-3 Example 3
Division Property of Inequality | graphing | solving inequalities
E
PTS: 1
DIF: L2
REF: 4-5 Compound Inequalities
4-5.1 Solving Compound Inequalities Containing And
NAEP 2005 A3a | NAEP 2005 A4c | ADP J.3.1
STA: 8NJ 4.5.E.1d | NJ 4.3.12 D.2a
4-5 Example 2
solving a compound inequality containing AND | compound inequality
B
PTS: 1
DIF: L2
REF: 4-5 Compound Inequalities
4-5.1 Solving Compound Inequalities Containing And
NAEP 2005 A3a | NAEP 2005 A4c | ADP J.3.1
STA: 8NJ 4.5.E.1d | NJ 4.3.12 D.2a
4-5 Example 2
solving a compound inequality containing AND | compound inequality
D
PTS: 1
DIF: L3
4-6 Absolute Value Equations and Inequalities
4-6.2 Solving Absolute Value Inequalities
NAEP 2005 N1g | NAEP 2005 A4a | NAEP 2005 A4c | ADP J.3.1
8NJ 4.5.E.1d | NJ 4.3.12 D.2a | NJ 4.3.12 C.1c
TOP: 4-6 Example 3
solving absolute value inequalities | graphing | solving a compound inequality containing OR
2
ID: A
19. ANS:
REF:
OBJ:
NAT:
STA:
KEY:
20. ANS:
REF:
OBJ:
NAT:
STA:
TOP:
KEY:
21. ANS:
OBJ:
NAT:
TOP:
22. ANS:
OBJ:
NAT:
TOP:
23. ANS:
OBJ:
NAT:
TOP:
KEY:
AND
24. ANS:
OBJ:
NAT:
TOP:
KEY:
D
PTS: 1
DIF: L3
4-6 Absolute Value Equations and Inequalities
4-6.2 Solving Absolute Value Inequalities
NAEP 2005 N1g | NAEP 2005 A4a | NAEP 2005 A4c | ADP J.3.1
8NJ 4.5.E.1d | NJ 4.3.12 D.2a | NJ 4.3.12 C.1c
TOP: 4-6 Example 3
solving absolute value inequalities | graphing | solving a compound inequality containing AND
A
PTS: 1
DIF: L3
4-3 Solving Inequalities Using Multiplication and Division
4-3.2 Using Division to Solve Inequalities
NAEP 2005 A4a | NAEP 2005 A4c | ADP J.3.1
NJ 4.3.12 D.2a | 8NJ 4.5.D.4 | 8NJ 4.5.E.1d | NJ 4.3.12 D.2a
4-3 Example 4
Division Property of Inequality | problem solving | word problem | solving inequalities
D
PTS: 1
DIF: L3
REF: 4-5 Compound Inequalities
4-5.1 Solving Compound Inequalities Containing And
NAEP 2005 A3a | NAEP 2005 A4c | ADP J.3.1
STA: 8NJ 4.5.E.1d | NJ 4.3.12 D.2a
4-5 Example 4
KEY: writing a compound inequality | compound inequality
E
PTS: 1
DIF: L3
REF: 4-5 Compound Inequalities
4-5.2 Solving Compound Inequalities Joined by Or
NAEP 2005 A3a | NAEP 2005 A4c | ADP J.3.1
STA: 8NJ 4.5.E.1d | NJ 4.3.12 D.2a
4-5 Example 4
KEY: writing a compound inequality | compound inequality
C
PTS: 1
DIF: L3
REF: 4-5 Compound Inequalities
4-5.1 Solving Compound Inequalities Containing And
NAEP 2005 A3a | NAEP 2005 A4c | ADP J.3.1
STA: 8NJ 4.5.E.1d | NJ 4.3.12 D.2a
4-5 Example 3
solving inequalities | problem solving | word problem | solving a compound inequality containing
A
PTS: 1
DIF: L2
REF: 4-5 Compound Inequalities
4-5.2 Solving Compound Inequalities Joined by Or
NAEP 2005 A3a | NAEP 2005 A4c | ADP J.3.1
STA: 8NJ 4.5.E.1d | NJ 4.3.12 D.2a
4-5 Example 5
solving a compound inequality containing OR | graphing | compound inequality
OTHER
25. ANS:
The solution to x < 3 OR x > 6 is all numbers less than 3 or greater than 6.
There is no solution to x < 3 AND x > 6 since a number cannot be less than 3 and greater than 6 at the same
time.
PTS:
OBJ:
NAT:
TOP:
KEY:
1
DIF: L3
REF: 4-5 Compound Inequalities
4-5.2 Solving Compound Inequalities Joined by Or
NAEP 2005 A3a | NAEP 2005 A4c | ADP J.3.1
STA: 8NJ 4.5.E.1d | NJ 4.3.12 D.2a
4-5 Example 5
solving a compound inequality containing OR | reasoning | writing in math
3