2

Chapter 9 Inequalities

Find .

7. / A = {2, 3, 4, 5, 6}, B = {3, 5} / 8. / A = {–2, 0, 2}, B = {–1, 0, 1} / 7.
8. / ______
______
9. / A = {1, 4, 9, 16}, B = {4, 6, 8} / 10. / A = {2, 4, 6}, B = {1, 3, 5} / 9.
10. / ______
______
11. / A = {2, 6, 8}, B = {6, 8, 10, 12} / 12. / A = {b, d, f, g}, B = {b, c, d, e, f } / 11.
12. / ______
______

Find .

13. / A = {2, 3, 4, 5, 6}, B = {3, 5} / 14. / A = {–4, –2, 0, 2}, B = {–1, 0, 1} / 13.
14. / ______
______
15. / A = {–2, –1, 0, 1, 2}, B = {1, 2, 3} / 16. / A = {2, 4, 6}, B = {1, 3, 5} / 15.
16. / ______
______
17. / A = {a, e, i, o, u}, B = {a, d, i, e, u } / 18. / A = {b, d, f, g}, B = {b, c, d, e, f } / 17.
18. / ______
______

Use set builder notation to write the set.

1. / Negative integers greater than –6 / 2. / Positive integers less than 8 / 1.
2. / ______
______
3. / Integers less than 15 / 4. / Even integers greater than 1 / 3.
4. / ______
______

Graph the solution set.

1. /
/ 2. /
/ 1.
2. / ______
______
3. /
/ 4. /
/ 3.
4. / ______
______
7. /
/ 8. /
/ 7.
8. / ______
______
9. /
/ 10. /
/ 9.
10. / ______
______
11. /
/ 12. /
/ 11.
12. / ______
______
13. /
/ 14. /
/ 13.
14. / ______
______
15. /
/ 16. /
/ 15.
16. / ______
______
17. /
/ 18. /
/ 17.
18. / ______
______

3

Solve and graph the solution set.

1. /
/ 2. /
/ 1.
2. / ______
______
3. /
/ 4. /
/ 3.
4. / ______
______
5. /
/ 6. /
/ 5.
6. / ______
______
9. /
/ 10. /
/ 9.
10. / ______
______

Solve.

11. / / 12. / / 13. / / 11.
12.
13. / ______
______
______
14. / / 15. / / 16. / / 14.
15.
16. / ______
______
______
17. / / 18. / / 19. / / 17.
18.
19. / ______
______
______
20. / / 21. / / 22. / / 20.
21.
22. / ______
______
______

Solve and graph the solution set.

1. /
/ 2. /
/ 1.
2. / ______
______
3. /
/ 4. /
/ 3.
4. / ______
______
5. /
/ 6. /
/ 5.
6. / ______
______
7. /
/ 8. /
/ 7.
8. / ______
______
9. /
/ 10. /
/ 9.
10. / ______
______

Solve.

14. / / 15. / / 16. / / 14.
15.
16. / ______
______
______
17. / / 18. / / 19. / / 17.
18.
19. / ______
______
______
20. / / 21. / / 22. / / 20.
21.
22. / ______
______
______

Solve.

3. / Three-fourths of a number is less
than or equal to twelve-twentieths.
Find the largest number that will
satisfy the inequality. / 4. / Four-fifths of a number is greater
than or equal to sixteen-fifteenths.
Find the smallest number that will
satisfy the inequality. / 3.
4. / ______
______
5. / A student must receive 360 points
out of 400 points on four tests to
receive an A in an accounting course.
One student’s results on the first three
tests were 94, 80, and 98. What scores
on the last test will enable the student to
receive an A in the course? / 6. / A student received a 72, and 82, a 93,
and an 84 on four tests in a sociology
course. What scores on the last test
will enable the student to receive a
minimum of 400 points? / 5.
6. / ______
______
7. / A sales manager for a computer
company receives payments of $1450,
$1870, and $1160 in commissions
during a three-month period. What is
the minimum commission the sales
manager must earn during the fourth
month in order to earn a minimum of
$5500 during the four-month period? / 8. / An electrician’s annual income for
the last four years was $38,630,
$30,960, $46,930, and $27,500. What
is the minimum annual income the
electrician must earn this year in order
to have earned $180,000 during the
five-year period? / 7.
8. / ______
______
9. / An appliance dealer will make a
profit on the sale of a freezer if the
cost of the new freezer is less than
80% of the selling price. What minimum price will enable the dealer to make
a profit on a freezer that costs the
dealer $480? / 10. / A new car dealer will make a profit
on the sale of a car if the cost of the
new car is less than of the selling
price. What minimum selling price will
enable the dealer to make a profit on a
car that costs the dealer $7200? / 9.
10. / ______
______

6

Solve.

1. / / 2. / / 3. / / 1.
2.
3. / ______
______
______
4. / / 5. / / 6. / / 4.
5.
6. / ______
______
______
10. / / 11. / / 12. / / 10.
11.
12. / ______
______
______
16. / / 17. / / 18. / / 16.
17.
18. / ______
______
______
19. / / 20. / / 21. / / 19.
20.
21. / ______
______
______

7

Solve.

3. / A rectangle is 9 ft wide and 2x – 3 ft
long. Express as an integer the
minimum length of the rectangle when
the area is greater than 207 ft2. (The
area of a rectangle is equal to its length
times its width.) / 4. / The base of a triangle is 12 in. and the
height is 2x – 6 in. Express as an
integer the maximum height of the
triangle when the area is less than
120 in.2 (The area of a triangle is equal
to one half the base times the height.) / 3.
4. / ______
______
5. / Company A rents cars for $10 a day
and 10¢ for every mile driven.
Company B rents cars for $28 a day
with unlimited mileage. What is the
maximum number of miles per day
you can drive a Company A car if it is
to cost you less than a Company B car? / 6. / Company A rents cars for $15 a day
and 15¢ for every mile driven.
Company B rents cars for $33 a day
with unlimited mileage. You want to
rent a car for one week. What is the
maximum number of miles you can
drive a Company A car if it is to cost
you less than a Company B car? / 5.
6. / ______
______
7. / An account executive earns $1200
per month plus 5% commission on the
amount of sales. The executive’s goal
is to earn a minimum of $3400 per
month. What amount of sales will
enable the executive to earn $3400
or more per month? / 8. / An account executive earns $600 per
month plus an 8% commission on the
amount of sales. The executive’s goal
is to earn a minimum of $2800 per
month. Find the minimum sales that
will enable the executive to earn $2800
per month. / 7.
8. / ______
______

8

Graph the solution set.

1. /
/ 2. /

3. /
/ 4. /

5. /
/ 6. /

7. /
/ 8. /