C4
Short Answer
Graph the inequality.
10.
–5 –4 –3 –2 –1
0
1
2
3
4
5
–5 –4 –3 –2 –1
0
1
2
3
4
5
1. d < 2
2. k > 9
2
11.
Solve the inequality.
3. x  –3
Solve the equation. If there is no solution, write
no solution.
12.
1
2
+x+
3
9
5
6
13. c – 12 > –1
4.
14.
5.
15. a + 8 – 2(a – 12) > 0
6.
16.
Write an inequality for the graph.
7.
Solve the compound inequality. Graph your
solution.
8. 2x – 2 < –12 or 2x + 3 > 7
9. Alexandria wants to go hiking on Saturday. To
choose from several parks she could go to, she
considers these conditions.
• She wants to hike for 2 hours.
• She wants to spend no more than 6 hours away
from home.
• She can average 65 miles per hour to and from the
park.
17.
Write a compound inequality that the graph
could represent.
0
1
2
3
4
5
18. Tina can type at least 60 words per minute. Write
and graph an inequality to model this situation.
Write an inequality to model the situation.
19. Thomas earned $44 or more.
20. A number exceeds 21.
Solve the inequality. Then graph your solution.
21.
Write and solve an inequality to find possible
distances from Alexandria’s home to a park that
satisfies the conditions.
–5 –4 –3 –2 –1
22.
23.
24.
25.
26. –2 < 4x – 10 < 6
27. The width of a rectangle is 33 centimeters. The
perimeter is at least 776 centimeters.
a. Write and solve an inequality to find the length
of the rectangle.
b. Write an inequality to find the area of the
rectangle.
Write a compound inequality that represents
each situation. Graph your solution.
28. all real numbers at least –6 and at most 3
C4
Answer Section
SHORT ANSWER
1. ANS:
–5 –4 –3 –2 –1
0
1
2
3
4
5
PTS: 1
DIF: L2
REF: 4-1 Inequalities and Their Graphs
OBJ: 4-1.2 Graphing and Writing Inequalities in One Variable NAT: NAEP 2005 A3a | ADP J.3.1
TOP: 4-1 Example 3
KEY: graphing | inequality
2. ANS:
–5 –4 –3 –2 –1
0
1
2
3
4
5
PTS: 1
DIF: L2
REF: 4-1 Inequalities and Their Graphs
OBJ: 4-1.2 Graphing and Writing Inequalities in One Variable NAT: NAEP 2005 A3a | ADP J.3.1
TOP: 4-1 Example 3
KEY: graphing | inequality
3. ANS:
–5 –4 –3 –2 –1
0
1
2
3
4
5
PTS: 1
DIF: L2
REF: 4-1 Inequalities and Their Graphs
OBJ: 4-1.2 Graphing and Writing Inequalities in One Variable NAT: NAEP 2005 A3a | ADP J.3.1
TOP: 4-1 Example 3
KEY: graphing | inequality
4. ANS:
n = 14 or n = –14
PTS: 1
DIF: L3
REF: 4-6 Absolute Value Equations and Inequalities
OBJ: 4-6.1 Solving Absolute Value Equations
NAT: NAEP 2005 N1g | NAEP 2005 A4a | NAEP 2005 A4c | ADP J.3.1
TOP: 4-6 Example 1
KEY: absolute value | Addition Property of Equality
5. ANS:
no solution
PTS: 1
DIF: L3
REF: 4-6 Absolute Value Equations and Inequalities
OBJ: 4-6.1 Solving Absolute Value Equations
NAT: NAEP 2005 N1g | NAEP 2005 A4a | NAEP 2005 A4c | ADP J.3.1
TOP: 4-6 Example 1
KEY: absolute value | Addition Property of Equality
6. ANS:
2
1
x = 4 or 5
3
3
PTS: 1
DIF: L3
REF: 4-6 Absolute Value Equations and Inequalities
OBJ: 4-6.1 Solving Absolute Value Equations
NAT: NAEP 2005 N1g | NAEP 2005 A4a | NAEP 2005 A4c | ADP J.3.1
TOP: 4-6 Example 2
7. ANS:
x = 13 or x = –13
KEY: absolute value | Division Property of Equality
PTS: 1
DIF: L3
REF: 4-6 Absolute Value Equations and Inequalities
OBJ: 4-6.1 Solving Absolute Value Equations
NAT: NAEP 2005 N1g | NAEP 2005 A4a | NAEP 2005 A4c | ADP J.3.1
TOP: 4-6 Example 1
KEY: absolute value | Addition Property of Equality
8. ANS:
x < –5 or x > 2
–5 –4 –3 –2 –1
0
1
2
3
4
5
PTS:
OBJ:
NAT:
KEY:
9. ANS:
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
TOP: 4-5 Example 5
solving a compound inequality containing OR | graphing | compound inequality
PTS:
OBJ:
NAT:
TOP:
KEY:
10. ANS:
1
DIF: L4
REF: 4-4 Solving Multi-Step Inequalities
4-4.1 Solving Inequalities With Variables on One Side
NAEP 2005 A3b | NAEP 2005 A3c | NAEP 2005 A4a | ADP J.3.1
4-4 Example 2
solving inequalities | problem solving | word problem | solving inequalities
PTS:
OBJ:
NAT:
KEY:
11. ANS:
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
TOP: 4-5 Example 4
writing a compound inequality | compound inequality
PTS: 1
DIF: L3
REF: 4-5 Compound Inequalities
OBJ: 4-5.1 Solving Compound Inequalities Containing And
NAT: NAEP 2005 A3a | NAEP 2005 A4c | ADP J.3.1
TOP: 4-5 Example 4
KEY: writing a compound inequality | compound inequality
12. ANS:
5
x
18
PTS:
OBJ:
NAT:
TOP:
KEY:
13. ANS:
1
DIF: L4
REF: 4-2 Solving Inequalities Using Addition and Subtraction
4-2.2 Using Subtraction to Solve Inequalities
NAEP 2005 N5e | NAEP 2005 A4a | NAEP 2005 A4c | ADP J.3.1
4-2 Example 3
Subtraction Property of Inequality | like terms | solving inequalities
c > 11
PTS:
OBJ:
NAT:
TOP:
14. ANS:
1
DIF: L2
REF: 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
4-2 Example 2
KEY: Addition Property of Inequality | solving inequalities
PTS: 1
DIF: L3
REF: 4-2 Solving Inequalities Using Addition and Subtraction
OBJ: 4-2.2 Using Subtraction to Solve Inequalities
NAT: NAEP 2005 N5e | NAEP 2005 A4a | NAEP 2005 A4c | ADP J.3.1
TOP: 4-2 Example 3
KEY: Subtraction Property of Inequality | solving inequalities | like terms
15. ANS:
a < –16
PTS:
OBJ:
NAT:
TOP:
KEY:
16. ANS:
1
DIF: L3
REF: 4-4 Solving Multi-Step Inequalities
4-4.1 Solving Inequalities With Variables on One Side | 4-1.1 Identifying Solutions of Inequalities
NAEP 2005 A3b | NAEP 2005 A3c | NAEP 2005 A4a | ADP J.3.1
4-4 Example 3
solving inequalities using the Distributive Property | solving inequalities | like terms
PTS:
OBJ:
NAT:
TOP:
17. ANS:
1
DIF: L3
REF: 4-4 Solving Multi-Step Inequalities
4-4.2 Solving Inequalities With Variables on Both Sides
NAEP 2005 A3b | NAEP 2005 A3c | NAEP 2005 A4a | ADP J.3.1
4-4 Example 4
KEY: solving inequalities
1
m 
2
PTS: 1
DIF: L2
REF: 4-1 Inequalities and Their Graphs
OBJ: 4-1.2 Graphing and Writing Inequalities in One Variable NAT: NAEP 2005 A3a | ADP J.3.1
TOP: 4-1 Example 4
KEY: writing an inequality from a graph | graphing
18. ANS:
0
10 20 30 40 50 60 70 80 90 100 110
PTS: 1
DIF: L3
REF: 4-1 Inequalities and Their Graphs
OBJ: 4-1.2 Graphing and Writing Inequalities in One Variable NAT: NAEP 2005 A3a | ADP J.3.1
TOP: 4-1 Example 5
KEY: translating an inequality | word problem | problem solving
19. ANS:
PTS: 1
DIF: L3
REF: 4-1 Inequalities and Their Graphs
OBJ: 4-1.2 Graphing and Writing Inequalities in One Variable NAT: NAEP 2005 A3a | ADP J.3.1
TOP: 4-1 Example 5
20. ANS:
n > 21
KEY: modeling with inequalities | translating an inequality
PTS: 1
DIF: L2
REF: 4-1 Inequalities and Their Graphs
OBJ: 4-1.2 Graphing and Writing Inequalities in One Variable NAT: NAEP 2005 A3a | ADP J.3.1
KEY: modeling with inequalities | translating an inequality
21. ANS:
–20 –16 –12 –8 –4
PTS:
OBJ:
NAT:
TOP:
22. ANS:
x > 32
0
0
4
8
12 16 20
1
DIF: L2
REF: 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
4-2 Example 1
KEY: Addition Property of Inequality | solving inequalities | graphing
10 20 30 40 50 60 70 80 90 100 110
PTS:
OBJ:
NAT:
KEY:
23. ANS:
1
DIF: L2
REF: 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
TOP: 4-3 Example 1
Multiplication Property of Inequality for c > 0 | graphing | solving inequalities
–10 –8 –6 –4 –2
PTS:
OBJ:
NAT:
KEY:
24. ANS:
–32
PTS:
OBJ:
NAT:
KEY:
25. ANS:
0
2
4
6
8
10
1
DIF: L2
REF: 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
TOP: 4-3 Example 2
Multiplication Property of Inequality for c < 0 | solving inequalities
–28 –24
–20 –16
–12
–8
–4
0
1
DIF: L2
REF: 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
TOP: 4-3 Example 1
Multiplication Property of Inequality for c > 0 | solving inequalities
–5 –4 –3 –2 –1
PTS: 1
0
1
2
3
DIF: L2
4
5
REF: 4-3 Solving Inequalities Using Multiplication and Division
OBJ: 4-3.2 Using Division to Solve Inequalities
NAT: NAEP 2005 A4a | NAEP 2005 A4c | ADP J.3.1
KEY: Division Property of Inequality | solving inequalities
26. ANS:
2<x<4
–10 –8 –6 –4 –2
PTS:
OBJ:
NAT:
KEY:
27. ANS:
0
2
8
10
;
1
DIF: L3
REF: 4-4 Solving Multi-Step Inequalities
4-4.1 Solving Inequalities With Variables on One Side
NAEP 2005 A3b | NAEP 2005 A3c | NAEP 2005 A4a | ADP J.3.1
4-4 Example 2
solving inequalities | problem solving | word problem | solving inequalities | multi-part question
–10 –8 –6 –4 –2
PTS:
OBJ:
NAT:
KEY:
6
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
TOP: 4-5 Example 2
solving a compound inequality containing AND | compound inequality
;
PTS:
OBJ:
NAT:
TOP:
KEY:
28. ANS:
4
TOP: 4-3 Example 3
0
2
4
6
8
10
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
TOP: 4-5 Example 1
writing a compound inequality | compound inequality