Inequalities
Name:
1.
Date:
Which of the following graphs shows the solution
set for the inequality shown below?
4.
Which of the following is the graph of the solution
of the inequality below?
jx + 1j < 4
jxj > 3
A.
A.
B.
B.
C.
C.
D.
D.
2.
Which of the following graphs represents the
solution of the inequality below?
jxj
2
A.
5.
B.
An inequality is shown below.
8
C.
12
Which of the following graphs represents the
solution of the inequality?
D.
A.
B.
3.
x+2
C.
The graph below is the solution of which of the
following inequalities?
D.
A.
jxj > 10
B.
jxj < 10
C.
x > 10
D. x < 10
page 1
6.
Which of the following absolute-value inequalities
best represents the graph shown on the number
line below?
9.
Look at the graph below.
Which of these inequalities has the solution set
that is shown in the graph?
7.
A.
jx
2j
3
B.
jx
2j
3
A.
2
x
3
B.
2<x<3
C.
jx
3j
2
D. jx
3j
2
C.
2
x<3
D.
2<x
10.
An inequality is shown below.
2 < 2x + 6
12
3
Which graph shows the solution for j2x + 3j
4?
A.
Which of the following graphs represents the
solution to the inequality?
B.
A.
C.
B.
D.
C.
D.
11.
What is the product of the solutions to the
equation j2x 1j = 3 ?
A.
8.
2
B.
2
C.
4
D.
4
Which of the following graphs best represents the
solution for the inequality below?
2 jxj
4
12.
A.
Which inequality describes the set of real numbers
modeled by this graph?
B.
C.
D.
page 2
A.
jxj
3
C.
jxj < 3
B.
jxj
3
D. jxj > 3
Inequalities
13.
What is the sum of the solutions to the equation
jx 3j = 2 ?
A.
1
B.
C.
6
D. there is no solution
16.
Which graph best represents the solution set to the
inequality shown below?
4
x+7
5
5
5
A.
B.
14.
C.
Which graph best represents the solution set to the
inequality?
jxj + 4
D.
10
A.
B.
C.
17.
D.
The speci cations for one of the bolts in a motor
require that the diameter of the bolt, in millimeters,
satis es the inequality jd 1:5j 0:027 .
Which of the following represents a bolt that could
not be used in this motor?
15.
A.
1.525 mm
B.
1.487 mm
C.
1.475 mm
D. 1.472 mm
Which of these best represents the solution of the
inequality shown below?
jx
2j
3
A.
18.
B.
C.
D.
page 3
Which of the following is the solution for
j3x 3j 9 > 27 ?
A.
x < 5 or x > 7
B.
x < 5 or x > 13
C.
x < 8 or x > 10
D. x < 11 or x > 13
Inequalities
19.
Which graph best represents the solution set for
j4x 2j < 10 ?
22.
A.
B.
A poll shows that it is likely that, with a margin
of error of 2 percentage points, 78% of those
randomly selected from a population would vote
for a particular candidate. This situation can be
described by the inequality jx 78j 2. Which
graph shows the percentage of voters (according to
the inequality) who favor the candidate?
A.
C.
B.
D.
C.
D.
20.
Which graph most appropriately represents the
solution set for j4x 2j < 10
A.
23.
B.
Look at this inequality.
jx + 5j
2
List all integer values of x that make the inequality
true.
C.
D.
24.
21.
Which graph shows the solution set for the
following inequality?
Select the correct representation of
2<x
3.
A.
x2 > x + 12
B.
A.
C.
B.
D.
C.
D.
page 4
Inequalities
25.
Use the inequality below to answer the following
question.
3 < 5x + 2
30.
12
what is the solution set for the equation
2x + jxj = 2?
A.
Which graph is the solution set to the compound
inequality?
f1g
B.
f 2g
C.
f 1g
D. f g
A.
B.
31.
What is the solution set of the equation
j2x + 5j 4 = 3?
32.
What is the solution set of the equation
x2 2x = 3x 6?
C.
D.
26.
A compound inequality is shown below.
5 < 2
3y < 14
What is the solution of the compound inequality?
A.
C.
4>y> 1
1>y>4
B.
28.
29.
f2; 3g
B.
C.
f 3g
D. f2; 3g
f2g
4<y< 1
D. 1 < y < 4
33.
27.
A.
What is the solution set for the equation
2x jx + 3j = 9?
A.
f12g
B.
C.
f2; 12g
D. fg
A.
C.
f2g
Find the positive value of x if j4
What is the solution set of the equation
j4a + 6j 4a = 10?
34.
2xj = 6.
What is the solution set for the equation
j3x 1j = x + 5?
A.
f 1g
B.
C.
f3g
D. f1; 3g
B.
1
2
The solution set of jx
A.
fx j x > 5g
B.
fx j x < 1g
C.
fx j 1 < x < 5g
D.
f0g
0; 21
2j < 3 is
D. fx j x < 1 or x > 5g
f 1; 3g
page 5
Inequalities
35.
The solution set of j2x
A.
fx j 5
B.
fx j x
C.
fx j 3
5j
40.
11 is
22g
x
8g
3_x
The solution to j3x
4j > 5 is
1
3
A.
x > 3 or x <
C.
x < 3 and x >
B.
1
3
x
D. x
3 or x
1
3
38.
The inequality j1:5C 24j 30 represents the
range of monthly average temperatures, C, in
degrees Celsius, for Toledo, Ohio. Solve for C.
B.
xj
C.
xjx
D.
39.
7
2
xj
xjx
1
2
7
2
43.
7
2
x
or x
1
B.
C.
( 2; 3]
D. [ 2; 3]
[ 2; 3)
What is the solution set of x2
A.
fx j x < 2 _ x > 6g
B.
fx j x < 6 _ x > 2g
C.
fx j 2 < x < 6g
8x + 12 < 0?
What is the solution set of the inequality
x2 6x 7 > 0?
A.
fx j 1 < x < 7g
B.
fx j x = 1 or x = 7g
C.
fx j x < 7 or x > 1g
or x
B.
0
What is the solution set of x2
7
2
A.
1
2
C.
C.
3
D.
7 or x
x
4
x
7
44. The solution of x2
Which value of a does not satisfy the inequality
jaj > 2a 3?
A.
( 2; 3)
1
2
x
1
2
A.
D. fx j x > 7 or x < 1g
What is the solution set of the inequality
j3 2xj 4?
A.
3 can be written as
D. fx j 6 < x < 2g
1
3
3 and x
42.
37.
x
8g
41.
36.
2
8g
x
D. fx j x
The inequality
5
page 6
4
B.
D.
3x
x
28
0?
7 or x
4
4<x<7
3x < 0 is
A.
0<x<3
B.
x>3
C.
x < 0 or x > 3
D. x < 0
Inequalities
45.
What is the solution set of the inequality
2x2 + 3x + 5 > 0 ?
A.
fx j 1 < x < 2:5g
B.
fx j 2:5 < x < 1g
C.
fx j x < 1 or x > 2:5g
48.
Which accompanying graph represents the solution
of the inequality x2 + 4x 21 < 0?
A.
B.
D. fx j x < 2:5 or x > 1g
C.

D. 
46.
6
5
4
3
2
1
0
1
2
3
7
6
5
4
3
2
1
0
1
2
3
7
6
5
4
3
2
1
0
1
2
3
7
6
5
4
3
2
1
0
1
2
3
!
!
…
!
!
…
Which is the graph of the solution of the
inequality (x 7)(x + 5) 0?
49.
A.
10
B.

C.

5
10
0
5
10
D. 
47.
7
0
5
10
0
5
0
5
5
5
5
10
10
10
10
B.
C.

D. 
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
4 > 0?
!
A.
!
…
B.
!
…
C.

!
…
D. 
Which graph represents the solution set of
x2 5x + 6 < 0?
A.
Which graph represents the inequality x2
50.
!
B.
!
…
C.
!
…

D. 
page 7
1
0
1
2
2
1
0
1
2
2
1
0
1
2
2
1
0
1
2
!
!
…
!
…
!
Which graph represents the solution set for the
inequality x2 x 20 < 0?
A.
!
2
5
4
3
2
1
0
1
2
3
4
5
5
4
3
2
1
0
1
2
3
4
5
5
4
3
2
1
0
1
2
3
4
5
5
4
3
2
1
0
1
2
3
4
5
!
!
!
…
!
…
Inequalities
51.
Which graph represents the solution set for
x2 + > 12?
A.

B.

C.

D. 
6
6
5
4
5
3
4
3
2
2
1 0
1
1 0
1
2
2
3
3
4
5
4
5
53.
6
6
6
5
4
3
2
1 0
1
2
3
4
5
6
6
5
4
3
2
1 0
1
2
3
4
5
6
4
3
2
1
0
1
2
x2
3
4
5
A.
x2
2x
8<0
B.
+ 2x
8<0
C.
x2
2x
8>0
D. x2 + 2x
8>0
3
2
1
0
1
2
3
4
5
6
Which inequality is represented by the graph
below?
!
…
A.
x2
2x
15 > 0
B.
2x
15 < 0
C.
x2
2x
15
D. x2 + 2x
15 < 0
!
…
0
x2
!
!
…
Which graph represents the solution of the
inequality x2 x 6 0 ?
A.
The accompanying graph represents the solution
set of which inequality?
5
4
!
…
54.
52.
5

B.
!
C.
D.
page 8

5
4
3
2
1
0
1
2
3
4
5
4
3
2
1
0
1
2
3
4
5
4
3
2
1
0
1
2
3
4
5
4
3
2
1
0
1
2
3
4
!
…
!
!
…
!
Inequalities
Problem-Attic format version 4.4.217
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_
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Inequalities
10/06/2014
1.
Answer:
B
21.
Answer:
B
2.
Answer:
A
22.
Answer:
D
3.
Answer:
A
23.
Answer:
4.
Answer:
B
24.
Answer:
A
5.
Answer:
A
25.
Answer:
C
6.
Answer:
A
26.
Answer:
B
7.
Answer:
B
27.
Answer:
A
8.
Answer:
D
28.
Answer:
5
9.
Answer:
D
29.
Answer:
B
10.
Answer:
B
30.
Answer:
B
11.
Answer:
B
31.
Answer:
f 6; 1g
12.
Answer:
D
13.
Answer:
32.
Answer:
D
D
14.
Answer:
33.
Answer:
A
A
15.
Answer:
34.
Answer:
C
A
16.
Answer:
35.
Answer:
C
B
17.
Answer:
36.
Answer:
A
D
18.
Answer:
37.
Answer:
D
19.
Answer:
38.
Answer:
C
A
20.
Answer:
39.
Answer:
C
A
7,
4
6,
C
5,
36
4,
3
Teacher's Key
40.
Answer:
Objective:
D
Algebra
41.
Answer:
C
42.
Answer:
D
43.
Answer:
A
44.
Answer:
A
45.
Answer:
A
46.
Answer:
B
47.
Answer:
A
48.
Answer:
A
49.
Answer:
C
50.
Answer:
A
51.
Answer:
A
52.
Answer:
B
53.
Answer:
B
54.
Answer:
A
Page 2