Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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Which number is a solution of the inequality?
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1.
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b > 11.3
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2.
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m > 
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3.
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x(7 – x) > 8
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4.
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5.
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Write the inequality in words.
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6.
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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. |
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7.
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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. |
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Graph the inequality.
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8.
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d < 2
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9.
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k > 
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10.
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11.
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x ³ –3
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Write an inequality for the graph.
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12.
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a. |  | b. | x <
–8 | c. | x > –8 | d. | x < 8 |
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13.
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14.
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Tina can type at least 60 words per minute. Write and graph an inequality to
model this situation.
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Write an inequality to model the situation.
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15.
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Thomas earned $44 or more.
a. | t > 44 | b. |  | c. | t < 44 | d. |  |
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16.
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A number exceeds 21.
a. |  | b. |  | c. | n >
21 | d. | n < 21 |
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Identify the graph of the inequality from the given description.
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17.
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x is negative.
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18.
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x is at least –4.5.
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Solve the inequality. Then graph your solution.
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19.
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20.
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x – 7 > –3.1
a. | x > –10.1
| c. | x > 4.1
 | b. | x > 3.9
 | d. | x > –4.1
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21.
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22.
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23.
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c – 3 > 6
a. | c < –9
 | c. | c >3
 | b. | c > 9
 | d. | c > –9
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24.
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a. | x > 
 | c. | x > 32
 | b. | x > 
 | d. | x > –4
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25.
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26.
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27.
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28.
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 v < 
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29.
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30.
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–2w < –18
a. | w > 9
 | c. | w < 9
 | b. | w < –16
 | d. | w > –16
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31.
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32.
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–2 < 4x – 10 < 6
a. | 4 < x < 12
 | c. | –16 < x <
–8
 | b. |  < x < 
 | d. | 2 < x
< 4
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33.
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34.
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a. | –36 < x < 14
 | c. | –17 > x >
8
 | b. | –17 < x < 8
 | d. | –8 < x < 8
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Solve the inequality.
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35.
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c – 12 > –1
a. | c > –13 | b. | c > 11 | c. | c >
13 | d. | c < –13 |
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36.
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37.
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38.
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39.
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–  x – 7 < 
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40.
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–5x – 7 < 28
a. | x > –7 | b. | x < –7 | c. |  | d. |  |
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41.
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a + 8 – 2(a – 12) > 0
a. | a < 32 | b. | a > –16 | c. | a <
–16 | d. | a > 32 |
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42.
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2(b – 8) > 12
a. | b > 20 | b. | b > 6 | c. | b > 14 | d. | b <
20 |
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43.
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44.
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12x – 3x + 11 > 4x – (17 –
9x)
a. | x > –7 | b. | x < 7 | c. |  | d. |  |
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45.
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46.
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47.
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What number would you subtract from each side of the inequality to solve
y +  > 16? a. | –16 | b. | 16 | c. |  | d. |  |
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48.
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Suppose you had d dollars in your bank account. You spent $22 but have at
least $28 left. How much money did you have initially? Write and solve an inequality that represents
this situation.
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49.
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Your class hopes to collect at least 325 cans of food for the annual food drive.
There were 132 cans donated the first week and 146 more the second week. a. Write an inequality that describes this situation. Let c
represent the number of cans of food that must be collected by the end of the third week for your
class to meet or surpass your goal.
b. How many cans are needed to meet or surpass your
goal? a. | 132 + 146 + c ³ 325; c £ 603 | c. | 132 + 146 + 325 ³ c;
c ³ 603 | b. | 132 + 146 + c ³ 325; c ³ 47 | d. | 132 + 146 + c > 325; c >
47 |
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50.
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Jeanette wants to tile the floor of a room in her house. The square tiles
measure  ft on each side. The room is 10 ft wide. a. Write
an inequality to describe how many tiles are needed to make one row of tiles across the width of the
room.
b. Solve the inequality.
c. How many tiles should Jeanette buy to form
one row?
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51.
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Replace  with a number that makes the inequalities
equivalent. –6 v <  ; v > –0.5
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52.
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The French club is sponsoring a bake sale. If their goal is to raise at least
$140, how many pastries must they sell at $3.50 each in order to meet that goal? Write and solve an
inequality.
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53.
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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.
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54.
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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.
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She wants to spend no more than 6 hours away from home.
• She can average 65 miles per hour
to and from the park.
Write and solve an inequality to find possible distances from
Alexandria’s home to a park that satisfies the conditions.
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Write a compound inequality that represents each situation. Graph your
solution.
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55.
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all real numbers that are greater than –6 but less than 6
a. | –6 £ x £
6
 | c. | –6 < x < 6
 | b. | –6 <
x < 6
 | d. | –6 < x £
6
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56.
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all real numbers at least –6 and at most 3
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57.
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On a road in the city of Rochester, the maximum speed is 50 miles per hour, and
the minimum speed is 20 miles per hour.
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Write a compound inequality that the graph could represent.
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58.
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59.
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60.
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A student scored 83 and 91 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
85 and 90.
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Write an inequality for the situation.
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61.
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all real numbers y that are less than 4 or greater than 9
a. | 4 < y < 9 | c. | y < 4 or y > 9 | b. | y < 4 or
y ³ 9 | d. | y
< 9 or y > 4 |
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62.
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all real numbers at most –9.5 or at least 5.5
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Solve the compound inequality. Graph your solution.
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63.
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2x – 2 < –12 or 2x + 3 > 7
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64.
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Solve the equation. If there is no solution, write no
solution.
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65.
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a. | x = 13 | c. | x = –1 | b. | x = 13 or x =
–13 | d. | no
solution |
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66.
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a. | n = 14 or n = –14 | c. | no solution | b. | n = 26 or
n = –30 | d. | n = 14 |
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67.
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a. | no solution | c. | j = –25 | b. | j = 15 or –15 | d. | j =
–15 |
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68.
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a. | no solution | c. | h = –7, h = 21 | b. | h =
21 | d. | h = 7, h =
–21 |
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69.
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a. | x =  or  | c. | x =  or  | b. | x =  | d. | no solution |
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70.
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a. | x = –7, x = 11 | c. | no solution | b. |  | d. |  |
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71.
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The ideal width of a safety belt strap for a certain automobile is 5 cm. An
actual width can vary by at most 0.35 cm. Write an absolute value inequality for the range of
acceptable widths.
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Short Answer
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72.
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Write four solutions to the inequality  .
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73.
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Eduardo solved –4x > 120 by adding 4 to each side of the
inequality. What mistake did he make?
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74.
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What number would you add to each side of the inequality to solve 13 <
4n – 14.4?
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Essay
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75.
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Suppose a classmate is having difficulty solving 4(x – 7) >
6x + 2 + 8x . Explain how to solve the inequality, showing all the necessary steps and
identifying the properties you would use.
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76.
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Three consecutive even numbers have a sum between 84 and 96. a. Write an inequality to find the three numbers. Let n
represent the smallest even number.
b. Solve the inequality.
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77.
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Suppose you start with at least $52 in your savings account and deposit $27 each
week. Write an inequality to describe how much money m you have after w weeks. If you
do this for 11 weeks, will you have enough to buy a bicycle that costs $340? Show your work.
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Other
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78.
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Are the solutions of the compound inequality x < 2 OR x > 5
different from the solutions to the compound inequality x < 2 AND x > 5 ?
Explain.
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79.
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Determine whether the following statement is sometimes, always or
never true. Explain your answer. If a > b and c > d,
then  .
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80.
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Explain why the equation  has no solution.
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