Name ________________________________________ Date __________________ Class __________________
MODULE
7
Inequalities
Module Quiz: B
7. There are 125 members in the school
marching band. The band wants to raise
$25,000 for a trip to a national
competition. The school agreed to
contribute $5,000 towards the trip. Which
inequality shows the amount of money
that each band member should raise?
1. What is a value of y that satisfies the
inequality below?
y
≤ 12
3
A 42
C 38
B 39
D 36
A 125x + 25,000 ≥ 5,000
2. Which of the following is a solution to the
inequality below?
B 125x + 5,000 ≥ 25,000
2x > 6
C 5,000x + 125 ≥ 25,000
A −3
C 3
B 2
D 5
D 5,000x + 25,000 ≥ 125
8. Which of the following is the solution to
the inequality −2 x − 4 ≤ 11 ?
3. Parvinder wants to save $500 for a trip.
Which inequality shows the least amount
she must save each month for 6 months
to accomplish this?
A 6x ≤ 500
C 6x ≥ 500
B 6x < 500
D
x ≥ 500 + 6
A
x ≤ −
15
2
C
x ≥ −
15
2
B
x ≤ −
7
2
D
x ≥ −
7
2
9. Which of the following ratios is not
equivalent to 2:10?
4. TJ earns a 20% commission on all sales
plus a base salary of $40,000. His total
income last year was more than $70,000.
Which inequality can be used to calculate
the minimum number of TJ’s sales?
A 40,000 + 0.2x ≥ 70,000
A
1
5
C
4
20
B
2
5
D
6
30
10. Which of the following values does not
satisfy the inequality −2x − 6 ≤ 1 ?
B 40,000 − 0.2x ≥ 70,000
C 0.2 + 40,000x ≥ 70,000
D 70,000 + 0.2x ≥ 40,000
5. Tony wants to buy a ticket for $15.75. He
has $9.25. How much must he earn to
buy the ticket?
A −4
C −2
B −3
D −1
11. Michele needs 30 ounces of pecans
to bake some pies. Pecans are sold in
4-ounce packages. Which inequality
could be used to find the least number of
packages of pecans she has to buy?
A at least $6.00
B less than $6.00
C at least $6.50
A
30
≤ 4
x
B
4
≤ 30
x
D at least $7.00
6. Peggy wants to run 5 miles in less than
60 minutes. What inequality shows what
her rate should be?
A 1 mi < 60 min
C 1 mi < 12 min
B 3 mi < 60 min
D 2 mi < 30 min
C 4x ≥ 30
D x ≤ 30 – 4
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
39
Name ________________________________________ Date __________________ Class __________________
MODULE
7
Inequalities
12. Solve the inequality. Show your work.
17. Solve the second inequality and graph
its solution on the number line.
x
≤1
6
________________________________________
________________________________________
18. Raja solved the inequality −3 x − 5 ≤ 1 .
His work is shown below.
Use the inequality for 13 and 14.
x+8≥5
13. Solve the inequality. Show your work.
________________________________________
________________________________________
Step 1:
−3x − 5 ≤ 1
Step 2:
−3x ≤ 6
Step 3:
x ≤ −2
Where did Raja make an error in his
calculation? Explain.
________________________________________
________________________________________
14. Graph the solution on the number line.
________________________________________
19. Joaquim earns a salary of $4,000 per
month plus a 6% commission on all of his
sales. He wants to earn at least $7,000
next month. Write an inequality that
shows what his total sales s must be in
order for Joaquim to reach his goal.
Use the inequalities for 15–17.
−3x > 9
3x > −9
15. Explain the difference between the two
inequalities. How does this affect your
method of solution?
________________________________________
________________________________________
20. Every month, the bank withdraws $15
from Betsy’s checking account as a
service fee. Betsy has budgeted $75 for
the next few service fees. For how many
months will the service fee be covered?
Write and solve an inequality to find the
solution. Show your work.
________________________________________
________________________________________
16. Solve the first inequality and graph its
solution on the number line.
________________________________________
________________________________________
________________________________________
________________________________________
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
40
MODULE 7 Inequalities
m
+6
2
16. three tenths of a number plus 5
15. Sample answer:
Module Quiz 7: B
1. D
17. 4 dimes = $0.40; some nickels = $0.05x;
0.4 + 0.05x = 2.25
2. D
3. C
18. x = 40
4. A
19. He divided 6 by 3 instead of −3 in Step 3.
5. C
20. 2,500 + 0.08s = 5,400
6. C
21. 50 − 12.25p
7. B
22. 50 + 12.50x = 400; x = 28
8. C
Module Quiz 6: D
9. B
1. B
10. A
2. A
11. C
3. C
12.
4. A
5. B
6. A
7. A
x
≤1
6
⎛x⎞
6 ⎜ ⎟ ≤ 6 (1)
⎝6⎠
x≤6
13. x + 8 ≥ 5
x+8−8≥5−8
x ≥ −3
8. A
9. C
10. B
14.
11. 5.50x ≤ 108.50 ; x ≤ 19.73; She can buy
19 shirts.
15. 20 nickels
15. To solve first inequality you have to divide
by a negative number, so you have to
reverse the inequality symbol. To solve
second inequality, you divide by a
positive number so the inequality symbol
stays the same.
16. $160
16. x < −3
12. x = −30
13. 4
14. 5x + 200 = 450; x = 50
17. In Step 2 she subtracted 4 instead of
adding 4.
17. x > −3
18. $40,000 + $1,000x = $60,000; x = 20
19. 200
18. He forgot to reverse the inequality symbol
in Step 3.
20. 100 + 20x = 400; x = 15
21. 2.75n = 80; n ≈ 29.09; He can ride the
train 29 times.
19. 4,000 + 0.06s ≥ 7,000
20. 15x ≤ 75
15 x 75
≤
15 15
x ≤ 5; Betsy can pay for no more than
5 months of the service fee.
2
⎛ 6 ⎞ 72
= 14
22. y = 12 ⎜ ⎟ =
5
⎝5⎠ 5
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162