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```					Chapter 3 Review

Multiple Choice
Identify the choice that best completes the statement or answers the question.

____    1. Describe the solutions of           in words.
a. The value of y is a number less than or equal to 3.
b. The value of y is a number greater than 4.
c. The value of y is a number equal to 3
d. The value of y is a number less than 4.
____    2. Graph the inequality m  –3.4.
a.
–5   –4   –3   –2   –1   0    1   2   3   4   5

b.
–5   –4   –3   –2   –1   0    1   2   3   4   5

c.
–5   –4   –3   –2   –1   0    1   2   3   4   5

d.
–5   –4   –3   –2   –1   0    1   2   3   4   5

____    3. Write the inequality shown by the graph.

–7       –6   –5   –4   –3   –2   –1   0   1   2   3   4   5   6   7   m

a. m  –3                                       c. m  –3
b. m  –3                                       d. m  –3
____    4. To join the school swim team, swimmers must be able to swim at least 500 yards without stopping. Let n
represent the number of yards a swimmer can swim without stopping. Write an inequality describing which
values of n will result in a swimmer making the team. Graph the solution.
a.

0        100 200 300 400 500 600 700 800 900 1000         n

b.

0        100 200 300 400 500 600 700 800 900 1000         n

c.

0    100 200 300 400 500 600 700 800 900 1000         n

d.

0    100 200 300 400 500 600 700 800 900 1000         n
____   5. Sam earned \$450 during winter vacation. He needs to save \$180 for a camping trip over spring break. He can
spend the remainder of the money on music. Write an inequality to show how much he can spend on music.
Then, graph the inequality.
a.                ;
s
–500       –400                –300              –200            –100             0             100   200       300   400   500

b.                               ;
s
–500       –400                –300              –200            –100             0             100   200       300   400   500

c.                               ;
s
–500       –400                –300              –200            –100             0             100   200       300   400   500

d.                               ;
s
–500       –400                –300              –200            –100             0             100   200       300   400   500

____   6. Solve the inequality n + 6  –1.5 and graph the solutions.
a. n  4.5

–10 –8       –6       –4       –2       0       2       4       6       8        10

b. n  –7.5

–10 –8       –6       –4       –2       0       2       4       6       8        10

c. n  –7.5

–10 –8        –6       –4       –2       0       2       4       6       8        10

d. n  4.5

–10 –8        –6       –4       –2       0       2       4       6       8        10

____   7. Carlotta subscribes to the HotBurn music service. She can download no more than 11 song files per week.
Carlotta has already downloaded 8 song files this week. Write, solve, and graph an inequality to show how
a. s  3

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

b. s  3

0     1      2        3        4        5       6       7       8       9       10        11

c. s  3

0      1     2         3        4        5       6       7       8       9       10    11
d. s  3

0        1        2        3       4           5       6        7        8        9       10    11

____   8. Denise has \$365 in her saving account. She wants to save at least \$635. Write and solve an inequality to
determine how much more money Denise must save to reach her goal. Let d represent the amount of money
in dollars Denise must save to reach her goal.
a.                ;                            c.                 ;
b.                ;                            d.                 ;
____   9. Solve the inequality and graph the solution.

a.            85
1

–9       –6       –3       0        3          6        9       12       15       18       21

b.            55
2

–9       –6       –3       0        3          6        9       12       15       18       21

c.            55
2

–9       –6       –3       0           3       6        9       12        15      18       21

d.            8
1
5

–9       –6       –3       0           3       6        9       12        15      18       21

____ 10. Solve the inequality                                        3 and graph the solutions.
a. x24

0                5                10              15                20               25         30    35        40    45   50

b. x 24

0                5                10              15                20               25         30    35        40    45   50

c. x      3
8

0            1         2           3           4            5        6            7         8     9   10    11    12

d. x 24

0                5            10                  15            20                   25         30    35        40    45   50

____ 11. Solve the inequality 2m  18 and graph the solutions.
a. m  9
–1      0        1         2        3         4       5        6        7     8        9        10    11

b. m  36

0   5    10       15       20   25    30      35      40       45   50   55   60       65    70   75   80   85   90   95

c. m 36

0   5    10       15       20   25    30      35      40       45   50   55   60       65    70   75   80   85   90   95

d. m  9

–1       0        1         2        3      4          5        6        7    8     9            10    11

____ 12. Solve the inequality                               2 and graph the solutions.
a. z  –8

–10 –8        –6       –4    –2       0     2       4       6        8    10

b. z  8

–10 –8       –6       –4    –2       0     2       4       6        8    10

c. z  8

–10 –8        –6       –4    –2       0     2       4       6        8    10

d. z  –8

–10 –8       –6       –4    –2       0     2       4       6        8    10

____ 13. Solve the inequality 2f  –8 and graph the solutions.
a. f  –4

–10 –8       –6       –4    –2       0     2       4       6        8    10

b. f  –4

–10 –8        –6       –4    –2       0     2       4       6        8    10

c. f  4

–10 –8        –6       –4    –2       0     2       4       6        8    10

d. f  4

–10 –8       –6       –4    –2       0     2       4       6        8    10
____ 14. Marco’s Drama class is performing a play. He wants to buy as many tickets as he can afford. If tickets cost
\$2.50 each and he has \$14.75 to spend, how many tickets can he buy?
a. 0 tickets                                      c. 6 tickets
b. 5 tickets                                      d. 4 tickets
____ 15. What is the greatest possible integer solution of the inequality             ?
a. 5.33                                           c. 6
b. 4                                              d. 5
____ 16. Solve the inequality n – 4  3 and graph the solutions.
a. n  –7

–10 –8    –6   –4   –2        0        2        4        6        8    10

b. n  –7

–10 –8   –6   –4   –2        0        2        4        6        8        10

c. n  1

–10 –8   –6   –4   –2        0        2        4        6        8        10

d. n  1

–10 –8    –6   –4   –2        0        2        4        6        8    10

____ 17. Solve the inequality z + 8  3 z  –4 and graph the solutions.
a. z  –3

–10 –8   –6   –4   –2        0        2        4        6        8        10

b. z  1

–10 –8    –6   –4   –2        0        2        4        6        8    10

c. z  –3

–10 –8    –6   –4   –2        0        2        4        6        8    10

d. z  1

–10 –8   –6   –4   –2        0        2        4        6        8        10

____ 18. A family travels to Bryce Canyon for three days. On the first day, they drove 150 miles. On the second day,
they drove 190 miles. What is the least number of miles they drove on the third day if their average number of
miles per day was at least 180?
a. 540 mi                                      c. 201 mi
b. 180 mi                                      d. 200 mi
____ 19. Solve and graph               .
a. x > 5

–13 –12 –11 –10 –9        –8       –7       –6       –5       –4       –3    –2   –1   0   1   2   3   4   5   6   7   8   9   10   11   12   13
b. x < 5

–13 –12 –11 –10 –9      –8   –7   –6   –5   –4   –3       –2   –1   0   1   2   3   4   5   6   7    8   9   10   11   12   13

c. x > 3

–13 –12 –11 –10 –9      –8   –7   –6   –5   –4   –3       –2   –1   0   1   2   3   4   5   6   7    8   9   10   11   12   13

d. x < –5

–13 –12 –11 –10 –9      –8   –7   –6   –5   –4   –3       –2   –1   0   1   2   3   4   5   6   7    8   9   10   11   12   13

____ 20. Mrs. Williams is deciding between two field trips for her class. The Science Center charges \$135 plus \$3 per
student. The Dino Discovery Museum simply charges \$6 per student. For how many students will the Science
Center charge less than the Dino Discovery Museum?
a. 132 or more students                         c. More than 45 students
b. 132 or fewer students                        d. Fewer than 45 students
____ 21.            Solve the inequality and graph the solution.

a.

–10 –9   –8   –7   –6   –5   –4   –3   –2   –1    0        1    2   3   4   5   6   7   8   9   10

b.

–10 –9   –8   –7   –6   –5   –4   –3   –2   –1    0        1    2   3   4   5   6   7   8   9   10

c.

–10 –9   –8   –7   –6   –5   –4   –3   –2   –1   0        1    2    3   4   5   6   7   8   9   10

d.

–10 –9   –8   –7   –6   –5   –4   –3   –2   –1   0        1    2    3   4   5   6   7   8   9   10

____ 22. Solve the inequality                                          .
a. z  2 9                                                                 c. all real numbers
16
b. z  3 7                                                               d. no solutions
16

____ 23. Solve                                 .
a.                                                c.
b.                                                d.
____ 24. Fly with Us owns a D.C.10 airplane that has seats for 240 people. The company flies this airplane only if
there are at least 100 people on the plane. Write a compound inequality to show the possible number of
people in a flight on a D.C.10 with Fly with Us. Let n represent the possible number of people in the flight.
Graph the solutions.
a.
–250        –200            –150          –100               –50           0           50           100        150       200   250

b.
–250        –200            –150          –100               –50           0           50           100        150       200   250

c.
–250        –200            –150          –100               –50           0           50           100        150       200   250

d.
–250        –200            –150          –100               –50           0           50           100        150       200   250

____25. Solve and graph the solutions of the compound
inequality                   .
a.   AND
0          1         2        3         4         5

b.          AND
0          1         2        3         4         5

c.          AND
0          1         2        3         4         5

d.          AND
0          1         2        3         4         5

____ 26. Solve and graph the compound inequality.
OR
a.           OR

–10 –9    –8       –7   –6   –5   –4   –3       –2   –1    0    1   2       3   4   5    6   7     8   9   10     s

b.               OR

–10 –9    –8        –7   –6   –5   –4   –3       –2   –1    0    1   2       3   4   5    6   7    8    9   10     s

c.               OR

–10 –9    –8        –7   –6   –5   –4   –3       –2   –1    0    1   2       3   4   5    6   7    8    9   10     s

d.               OR

–10 –9    –8       –7   –6   –5   –4   –3       –2   –1    0    1   2       3   4   5    6   7     8   9   10     s
____ 27. Write the compound inequality shown by the graph.

–10 –9    –8   –7   –6   –5   –4   –3   –2   –1    0        1        2        3       4         5        6        7        8        9        10     x

a.          AND                                c.           OR
b.        AND                                  d.           OR
____ 28. Which of the following is a solution of          AND              ?
a. 2                                           c. 12
b. 14                                          d. –6
____ 29. Solve the inequality                  and graph the solutions. Then write the solutions as a compound
inequality.
a.
–27 –24 –21 –18 –15 –12 –9          –6   –3        0        3        6       9       12        15       18       21    24        27       30

b.
–30 –27 –24 –21 –18 –15 –12 –9            –6   –3        0        3        6       9        12       15       18       21        24       27     30

c.
–27 –24 –21 –18 –15 –12 –9          –6   –3        0        3        6       9       12        15       18       21    24        27       30

d.
–30 –27 –24 –21 –18 –15 –12 –9            –6   –3        0        3        6       9        12       15       18       21    24        27       30

____ 30. Solve and graph the solutions of                                                                 . Write the solutions as a compound inequality.
a. –9 < x < 21
–24 –22 –20 –18 –16 –14 –12 –10 –8             –6           –4       –2       0       2         4        6        8    10       12        14     16      18   20   22   24

b. x < – 15 OR x > 15

–24 –22 –20 –18 –16 –14 –12 –10 –8             –6           –4       –2       0       2         4        6        8    10        12       14     16      18   20   22   24

c. x > 21

–24 –22 –20 –18 –16 –14 –12 –10 –8                –6       –4       –2       0        2        4        6        8        10       12     14       16   18   20   22   24

d. x < – 9 OR x > 21

–24 –22 –20 –18 –16 –14 –12 –10 –8             –6           –4       –2       0       2        4         6        8    10       12       14     16       18   20   22   24

Numeric Response

31. What is the least possible integer solution of the inequality                                                                                                       ?

32. A volleyball team scored 14 more points in its first game than in its third game. In the
second game, the team scored 28 points. The total number of points scored was less
than 80. What is the greatest number of points the team could have scored in its first
game?
Chapter 3 Review

MULTIPLE CHOICE

1. ANS: D
Test values of y that are positive, negative, and 0.

When the value of y is a number less than 4, the value of       is less than 10.
When the value of y is 4, the value of     is equal to 10.
When the value of y is a number greater than 4, the value of          is greater than 10.

It appears that the solutions of           are numbers less than 4.

Feedback
A    Test the value you found with the equal sign. Do you get a true statement?
B    Test some values and find out if you get a true statement. Then, check the inequality
symbol.
C    Is this the only solution? Test some more values, including fractions.
D    Correct!

2. ANS: B
The graph should start at the given value. A > or < graph has an empty circle at that value. A or graph has
a solid circle at that value. A > or graph has an arrow to the right, and a < or graph has an arrow to the
left.

Feedback
A    Check the direction the arrow should be pointing.
B    Correct!
C    Check the direction the arrow should be pointing.
D    A "greater than" or "less than" graph has an empty circle. A "greater than or equal to" or
"less than or equal to" graph has a solid circle.

3. ANS: C
Use the variable m. The arrow points to the right, so use either > or . The solid circle at –3 means that –3 is a
solution, so use .

Feedback
A    The arrow should point in the same direction as the inequality symbol.
B    The endpoint is not a solution.
C    Correct!
D    The endpoint is not a solution.
4. ANS: D
The variable n must be greater than or equal to 500 yards for a swimmer to make the team. The graph should
include the number 500 (solid circle at 500) and all the numbers to the right of 500 on the number line.

Feedback
A          The number of yards must be greater than or equal to 500, not less than 500.
B          The number of yards must be greater than or equal to 500, not less than 500.
C          The number 500 should be included in the solution.
D          Correct!

5. ANS: C
Sam has \$450, but must save \$180 of that for his camping trip.
If s is the amount he can spend on music, then

So,                 .
s
–500     –400        –300         –200       –100         0    100   200       300   400   500

Feedback
A          The amount Sam can spend on music cannot be more than the amount he earned.
B          The amount Sam can spend on music cannot be more than what he saved after his
camping trip.
C          Correct!
D          Sam has \$450, but must save \$180 for his trip. The remaining amount is how much he
can spend on music.

6. ANS: C
n + 6  –1.5
–6 –6                                                   Subtract 6 on both sides to isolate n.
n  –7.5

–10 –8    –6       –4   –2   0     2    4     6      8   10

Use a solid circle when the value is included in the graph, such as with or  Use an empty circle when the
value is not included, such as with > or <.

Feedback
A          Use a solid circle for a "greater than or equal to" or "less than or equal to" graph. Use an
empty circle for a "greater than" or "less than" graph.
B          Check that the arrow is pointing in the correct direction.
C          Correct!
D          Check that you used the correct inverse operation.
7. ANS: C
8                              +                 s                  11

Subtract 8 from both sides to undo the addition.
s                           3

Since you can only download whole songs, graph the nonnegative integers less than or equal to 3.

0   1   2   3   4   5   6   7   8   9   10   11

Feedback
A       Check the inequality symbol.
B       Check the graph, as it not reasonable to have a fractional number of songs.
C       Correct!
D       Check the graph, as it not reasonable to have a fractional number of songs.

8. ANS: A
Let d represent the amount of money in dollars Denise must save to reach her goal.
\$365             plus     additional amount of money is at least             \$635
in dollars
365              +                     d                                     635

Since 365 is added to d, subtract 365 from both sides to undo the
365
365

Check the endpoint 270 and a number that is greater than the endpoint.

Feedback
A       Correct!
B       You should be solving an inequality, not an equation.
C       Subtract from both sides of the inequality.
D       Check the endpoint to see if you get a true statement.
9.   ANS: B
Step 1: Rewrite both mixed numbers as improper fractions.
and

Step 2: Solve the inequality.
Rewrite the inequality.
Subtract              from both sides.
Rewrite the fractions with a common denominator.
2
=5       5
Simplify.

Step 3: Graph the inequality.

–9    –6   –3       0    3   6    9   12    15   18    21

Feedback
A        To solve the inequality, subtract the first mixed number from both sides of the
inequality.
B        Correct!
C        Check the direction of the inequality.
D        To solve the inequality, subtract the first mixed number from both sides of the
inequality.

10. ANS: A
3
Multiply both sides by 8 to isolate x.
 3(8)
x  24


0         5            10       15        20     25         30    35    40    45   50

Use a solid circle when the value is included in the graph, such as with or  Use an empty circle when the
value is not included, such as with > or <.

Feedback
A        Correct!
B        Use a solid circle when the value is included in the graph. Use an empty circle when the
value is not included.
C        To solve the inequality, use multiplication to undo the division.
D        Check that the arrow is pointing in the correct direction.
11. ANS: D
2m  18
                           Divide both sides by 2 to isolate m.
m9
Use a solid circle when the value is included in the graph, such as with or  Use an empty circle when the
value is not included, such as with > or <.

–1     0        1        2     3    4       5       6       7    8   9   10   11

Feedback
A        Check that the arrow is pointing in the correct direction.
B        To solve the inequality, use division to undo the multiplication.
C        Use a solid circle when the value is included in the graph. Use an empty circle when the
value is not included.
D        Correct!

12. ANS: D
2
Multiply both sides by –4 to isolate z. When you multiply by a
 2(–4)
negative number, reverse the inequality symbol.
z  –8
Use a solid circle when the value is included in the graph, such as with or  Use an empty circle when the
value is not included, such as with > or <.

–10 –8     –6       –4   –2     0   2   4       6       8   10

Feedback
A        When multiplying by a negative number, reverse the inequality symbol.
B        Check the signs.
C        Check the signs.
D        Correct!
13. ANS: A
2f  –8
                 Divide both sides by 2 to isolate f.
f  –4
Use a solid circle when the value is included in the graph, such as with or  Use an empty circle when the
value is not included, such as with > or <.

–10 –8   –6   –4   –2   0   2   4   6   8   10

Feedback
A      Correct!
B      When dividing by a positive number, keep the same inequality symbol. When dividing
by a negative number, reverse the inequality symbol.
C      Check the signs.
D      Check the signs.

14. ANS: B

Divide both sides by the ticket price. The inequality symbol does not
change.
Simplify.
5 is the largest whole number less than 5.9.

Feedback
A      Divide the total amount by the ticket price and round down to the nearest whole
number.
B      Correct!
C      Round down, not up, to the nearest whole number.
D      Divide the total amount by the ticket price and round down to the nearest whole
number.

15. ANS: D
With estimation,                  becomes                   . So, the greatest possible integer solution is 5.

Feedback
A      The solution needs to be an integer.
B      Round the numbers in the inequality to the nearest integer, and then divide.
C      Round the numbers in the inequality to the nearest integer, and then divide.
D      Correct!

16. ANS: B
Use inverse operations to undo the operations in the inequality one at a time.
n – 4  3
n  –7
–10 –8   –6   –4   –2   0   2    4   6     8   10

Use a solid circle when the value is included in the graph, such as with or  Use an empty circle when the
value is not included, such as with > or <.

Feedback
A     If you divide both sides of the inequality by a negative number, reverse the inequality
symbol. If you divide by a positive number, do not reverse the inequality symbol.
B     Correct!
C     Use inverse operations to undo the operations in the inequality one at a time.
D     Check your calculations when using inverse operations to isolate the variable.

17. ANS: C
z + 8  3 z  –4
4z + 8  –4                          Combine like terms.
4z  –12                             Subtract 8 from both sides.
Divide both sides by 4. When you divide by a negative number,
z  –3                              reverse the inequality symbol. When you divide by a positive
number, keep the same inequality symbol.

–10 –8   –6   –4   –2   0   2   4    6     8   10

Use a solid circle when the value is included in the graph, such as with or  Use an empty circle when the
value is not included, such as with > or <.

Feedback
A     If you divide both sides of the inequality by a negative number, reverse the inequality
symbol. If you divide by a positive number, keep the same inequality symbol.
B     Use inverse operations to isolate the variable.
C     Correct!

18. ANS: D
Let d represent the distance the family drove on the third day. The average number of miles is the sum of the
miles of each day divided by 3.
( 150       plus        190       plus       d)        divided      3        is at    180
by                 least
( 150        +          190        +         d)           ÷         3                 180

Since              is divided by 3, multiply both sides by 3 to
undo the division.

Combine like terms.
Since 340 is added to d, subtract 340 from both sides to undo
The least number of miles the family drove on the third day is 200.

Feedback
A     First, set up an inequality where the average number of miles is the sum of the miles of
each day divided by 3. Then, solve the inequality.
B     First, set up an inequality where the average number of miles is the sum of the miles of
each day divided by 3. Then, solve the inequality.
C     First, set up an inequality where the average number of miles is the sum of the miles of
each day divided by 3. Then, solve the inequality.
D     Correct!

19. ANS: B

Subtract 3x from both sides to collect the x terms on one side of the
3x < 15
inequality symbol.
x<5                        Divide both sides by 3.

–13 –12 –11 –10 –9   –8   –7   –6   –5   –4   –3    –2   –1    0       1   2   3     4   5   6   7    8   9   10   11   12   13

Feedback
A     Only change < to > when you divide or multiply by a negative number.
B     Correct!
D     Check your positive and negative signs.

20. ANS: C
Science       plus             \$3             per             student              is less       \$12          per            student
Center fee                                                                           than
\$135           +              \$3                                  s                  <          \$6                               s

135 + 3s < 6s
– 3s – 3s
135     < 3s

<
45 < s

If 45 < s, then s > 45. The Science Center charges less if there are more than 45 students.

Feedback
A     The per-student fees need to be multiplied by the number of students.
B     The per-student fees need to be multiplied by the number of students.
C     Correct!
D     This is the number of students where the Dino Discovery Museum charges less.
21. ANS: B
On the left side, combine the two terms. On the right side, distribute 1.5.



Subtract the 1.5x from both sides of the inequality.
           6

Divide both sides of the inequality by      . Reverse the inequality symbol.
3

Feedback
A     Check your signs. When you subtract 1.5 from both sides you should have a negative
coefficient.
B     Correct!
C     Check your signs. When you subtract 1.5 from both sides you should have a negative
coefficient. When multiplying or dividing by a negative number, reverse the inequality
symbol.
D     Reverse the inequality symbol when multiplying or dividing both sides of an inequality
by a negative number.

22. ANS: C
When the inequality is simplified, if the result is a statement that is always true, then the solution set includes
all real numbers. If the result is a statement that is always false, then there are no solutions to the inequality.

Feedback
A     Check that you have simplified the inequality correctly.
B     Check that you have simplified the inequality correctly.
C     Correct!
D     Check whether any real number will make the inequality true or whether no real
numbers will make the inequality true.

23. ANS: D

Combine like terms.
Simplify.
Divide both sides by 0.5.

Feedback
A     The inequality symbol will only change if you multiply or divide by a negative number.
B     Combine only like terms.
C     When moving a term from one side of the inequality to the other side, subtract from
both sides.
D     Correct!
24. ANS: A
Let n represent the possible number of people in the flight.
100       is less than or equal to     n         is less than or equal to                                               240
100                                    n                                                                                240

–250        –200         –150          –100             –50           0           50           100       150       200     250

Feedback
A       Correct!
B       The phrase "at least" means the number 100 is included in the solution.
C       Check your inequality symbols. Is it possible for a number to be less than or equal to
100 AND greater than or equal to 240?
D       A compound inequality is the result of combining two simple inequalities into one
statement by the words AND or OR.

25. ANS: C
AND                                                Write the compound inequality using AND.
Solve each simple inequality.
Divide to undo the multiplication.
AND

First, graph the solutions of each simple inequality. Then, graph the intersection by finding where the two
graphs overlap.

Feedback
A       Check the endpoints to see whether they are included in the solutions.
B       Check the endpoints to see whether they are included in the solutions.
C       Correct!
D       Check the inequality symbols. A number cannot be less than 1 AND greater than or
equal to 4.

26. ANS: D
First solve each simple inequality to obtain                                        OR        . The graph of the compound inequality is the
union of the graph of          and the graph of                                     . Find the union by combining the two regions.

–10 –9    –8    –7   –6   –5   –4   –3     –2   –1    0    1   2       3   4   5    6   7     8   9   10    s

Feedback
A       Use a solid circle if and only if the endpoint is contained in the solution set.
B       Find the union of the two regions. Use a solid circle if and only if the endpoint is
contained in the solution set.
C       Find the union of the two regions.
D       Correct!
27. ANS: C

–10 –9   –8   –7   –6   –5   –4   –3    –2    –1       0       1       2       3        4        5        6        7        8        9    10   x

x –5                                              OR                                                                         x>3
The numbers to the left of –5                         The shaded area is not                                               The numbers to the right of 3 are
A solid circle is used.                               the compound inequality                                              An empty circle is used.
This part of the inequality                           uses OR.                                                             This part of the inequality uses >.
uses 

Feedback
A      The shaded portion is not between two numbers.
B      The shaded portion is not between two numbers.
C      Correct!
D      There is a closed dot at –5.

28. ANS: A
Test each value to see which is a solution of                                                                  AND                                  .

If x = 14, then                       AND                                      . The first inequality is false, so the compound inequality is false.

If x = 12, then                       AND                                      . The first inequality is false, so the compound inequality is false.

If x = –6, then                       AND                                      . The second inequality is false, so the compound inequality is
false.

If x = 2, then                    AND                                  . Both inequalities are true, so the compound inequality is true.

Feedback
A      Correct!
B      Substitute the solution into the inequalities to check that the compound inequality is
true.
C      Check the inequality symbols.
D      As the compound inequality is an "AND" statement, check that both inequalities are
true.

29. ANS: C

Add 9 to isolate the absolute-value expression.
Think: What numbers have an absolute value less than 8?
AND                                        is between –8 and 8, inclusive.
AND                                           Solve the two inequalities.
Write the solution as a compound inequality.

–27 –24 –21 –18 –15 –12 –9            –6    –3    0       3       6       9       12       15       18       21       24       27       30
Feedback
A       Isolate the variable to find the solution of the original inequality.
B       Check the inequality symbols.
C       Correct!
D       The inequality contains an absolute-value expression, so the solution should be a
compound inequality.

30. ANS: D

Add 3 to both sides to undo the subtraction and isolate the
absolute value.
Think: “What numbers have an absolute value less than –15
x – 6 < –15 OR x – 6 > 15
or greater than 15?”
x < – 9 OR x > 21                      Solve the two inequalities.

–26 –24 –22 –20 –18 –16 –14 –12 –10 –8   –6   –4   –2   0   2   4   6   8   10   12   14   16   18   20   22   24   26

Feedback
A       First, isolate the absolute value. Then, solve two separate inequalities.
B       First, isolate the absolute value. Then, solve two separate inequalities.
C       First, isolate the absolute value. Then, solve two separate inequalities.
D       Correct!

NUMERIC RESPONSE

31. ANS: 5

32. ANS: 18

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