Download Solving Compound Inequalities

Name ________________________________________ Date __________________ Class__________________
LESSON
5-3
Practice A
Solving Compound Inequalities
Graph each inequality, and then graph the compound inequality.
1. x ! 3
2. z 0
xd4
z!2
intersection: x ! 3 AND x d 4
union: z 0 OR z ! 2
Write the compound inequality shown by each graph.
3.
4.
_________________________________________
________________________________________
Fill in the blanks to solve each compound inequality.
Graph the solutions.
5. n 5 2
OR
_____ _____
n _____
OR
n5t9
6. 11 d 2x 1 d 1
_____ _____
11 d 2x 1
n t _____
AND
_____ _____
_____
d 2x
_____
AND
y _____ y _____
_____
dx
2x 1 d 1
2x d _____
y _____
AND
_____
y _____
x d _____
Write a compound inequality for each problem. Graph the solutions.
7. To relieve arthritis, Dr. Stoll recommends taking
between 400 and 600 mg of ibuprofen, inclusive.
_____________________________________
8. An advertisement for a part-time job says that the
hourly rate is between $6.40 and $9.80 inclusive,
depending on experience.
_____________________________________
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113
Holt McDougal Coordinate Algebra
4. all real numbers
6.
x3
3x 11
5. n ! 12
y1
6. no solutions
5
7. x d 5
7
x
y
x
y
4
7
4
1
2
5
3
2
0
3
2
5
2
1
1
8
4
1
0
11
8. z 0
9. no solutions
10. b ! 11
11. k ! 1
1
3
y2
12. d 610
13. decreased 2000 people each year
14. 350,000 2000y
15. increased 3000 people each year
16. 200,000 3000y
17. 350,000 2000y 200,000 3000y
y ! 30 for years after 2010
Review for Mastery
1. add 6y to both sides
x d 2
2. add 3p to both sides
3. add 3r to both sides
Problem Solving
4. c ! 4
5. x 1. 5r ! 50 2r ; r ! 16
3
2
2. 25,000 1000y ! 19,000 1500y; y 12
3. 75m ! 510 60m; m ! 34
6. a ! 15
4. 15 5s ! 8s ; s 5
7. no solutions
5. B
8. all real numbers
6. F
Reading Strategies
9. all real numbers
10. all real numbers
1. Left; so he divides by a positive number.
11. no solutions
2. t ! 8
Challenge
3. n ! 7; left; you do not have to switch the
inequality symbol.
1. x
4; the lines intersect
2. x 4; the line for y1 is above
(greater than) the line for y2
5-3 SOLVING COMPOUND
INEQUALITIES
3. x 3 ! 2x 1
Practice A
4. x 4; same solutions as problem 2
1.
5. Possible answer: Find the x-values for
which the line for y2 is either above
(greater than) or intersects (equal to) the
line for y1. The solutions are x t 4.
© Houghton Mifflin Harcourt Publishing Company
A17
Holt McDougal Coordinate Algebra
12. 140 w d 147
2.
Practice C
1. 0.5 x 2
3. x d 1 OR x t 5
4. x ! 4 AND x d 1
2. a d 1 OR a t 6
5. 5; 5; 5; 5; 3; 4
3. y ! 8 OR y d 3; all real numbers
6. 1; 1; 1; 1; 10; 2; 2; 2; 2; 2; 5; 1
4. 4 d x d 1
7. 400 d m d 600
5. k ! 3
8. 6.40 d r d 9.80
6. z 14 OR z t 1.8
Practice B
1. 2 x 4
2. x 3 OR x t 3
3. x d15 OR x t 8
4. 0 d x 20
7. 8 d n d 10
5. 7 x 4
8. p ! 2 AND p d 6; no solutions
6. 3 d n 7
9. 0 A 4.55 OR A ! 8.75
7. 3 d b d 2
Review for Mastery
8. x 0 OR x t 6
1. 3 x 4
x 4 d 10
2. 8 d m 4
m 4 d 15
3.
9. k d 4 OR k t 4
10. s d 2 OR s ! 7
11. 20 d h d 20,000
4. 4 k 1
© Houghton Mifflin Harcourt Publishing Company
A18
Holt McDougal Coordinate Algebra