Name
LESSON
Date
Class
Problem Solving
11-5 Introduction to Inequalities
Write the correct answer.
The American College of Sports
Medicine recommends exercising at an
intensity of 60% to 90% of your
maximum heart rate.
Heart Rates by Age
1. Mara is 25 years old. Write a
compound inequality to represent her
target heart rate range while bike
riding.
2. Leia is 38 years old. Write a
compound inequality to represent the
zone between her maximum heart
rate and the upper end of her target
range.
Age
Maximum
Heart Rate
Target Range
20–24
200
120–180
25–29
195
117–176
30–34
190
114–171
35–39
185
111–167
40–44
180
108–162
3. Rudy is 42 years old. Write an
inequality to represent at least 70%
of his maximum heart rate.
4. Write a compound inequality to represent 60% to 90%
of your maximum heart rate in ten years.
Choose the letter for the graph that represents each statement.
5. Alena decided to pay not more than
$25 to get her old bike repaired.
A I
C III
B II
D IV
I.
5 10 15 20 25 30 35 40 45 50
0
5 10 15 20 25 30 35 40 45 50
0
5 10 15 20 25 30 35 40 45 50
0
5 10 15 20 25 30 35 40 45 50
II.
6. It was so cold last week that the
temperature never reached 25°F.
F I
H III
J IV
G II
III.
IV.
7. There were at least 25 people ahead
of Ivan in the cafeteria line.
A I
C III
B II
D IV
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0
8. The garden yielded more than
25 pounds of potatoes.
H III
F I
G II
J IV
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Holt Mathematics
Problem Solving
LESSON
11-5 Introduction to Inequalities
Challenge
LESSON
11-5 Square Equations
Some equations can be solved using square roots.
Write the correct answer.
Example 1:
Example 2:
Solve x 2 25.
8
w
Solve 2 w.
Think: 52 25, and (5)2 25.
First, cross multiply: w 2 16.
The American College of Sports
Medicine recommends exercising at an
intensity of 60% to 90% of your
maximum heart rate.
So, the equation has two solutions.
Think: 42 16, and (4)2 16.
x 5, 5
1. Mara is 25 years old. Write a
compound inequality to represent her
target heart rate range while bike
riding.
So, the equation has two solutions.
y 4, 4
Solve.
1. x 2 64
x 8, 8
y 9, 9
2
a 7, 7
c
3
7. 3 c
c 3, 3
t
10. t 4
t 6, 6
13. p 2 5 20
p 5, 5
n 11, 11
m 10, 10
k
25
8. 4 k
16
d
11. d 9
h 7, 7
z 6, 6
15. 29 v 2 110
v 9, 9
Holt Mathematics
117–176
30–34
190
114–171
35–39
185
111–167
40–44
180
108–162
I.
0
5 10 15 20 25 30 35 40 45 50
0
5 10 15 20 25 30 35 40 45 50
0
5 10 15 20 25 30 35 40 45 50
0
5 10 15 20 25 30 35 40 45 50
II.
6. It was so cold last week that the
temperature never reached 25°F.
F I
H III
J IV
G II
IV.
7. There were at least 25 people ahead
of Ivan in the cafeteria line.
A I
C III
B II
D IV
8. The garden yielded more than
25 pounds of potatoes.
H III
F I
G II
J IV
III.
46
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All rights reserved.
Holt Mathematics
Puzzles, Twisters & Teasers
LESSON
11-5 Hard to Swallow!
Find and circle words from the list in the word search
(horizontally, vertically or diagonally). Find a word that
answers the riddle. Circle it and write it on the line.
An inequality is a comparison of two unequal values. This chart will
help you understand both words and symbols for inequalities.
No more than 8 people can ride in the
elevator.
“No more than 8” Means “8 or less
than 8.”
Symbol for “less than or equal to 8”: 8
inequality
compound
value
symbol
graph
less
greater
equal
more
fewer
I
L
E
S
S
V
Y
H
A
L
Q
Inequalities
More than 25 students try out for the
team each year.
“More than 25” means “a number
greater than 25.”
Symbol for “greater than 25”: 25
195
x 0.7 180; x 126
5. Alena decided to pay not more than
$25 to get her old bike repaired.
A I
C III
B II
D IV
Reading Strategies
LESSON
11-5 Connecting Words and Symbols
The team has scored fewer than 5 runs
in each game.
“Fewer than 5” means “less than 5.”
Symbol for “less than 5”: 5
120–180
25–29
Choose the letter for the graph that represents each statement.
e 8, 8
45
200
Possible answer: 120 x 180
12. z 2 1 35
14. h 2 14 63
Target Range
20–24
167 x 185
s 13, 13
d 12, 12
Maximum
Heart Rate
4. Write a compound inequality to represent 60% to 90%
of your maximum heart rate in ten years.
e
16
9. 4 e
k 10, 10
Age
3. Rudy is 42 years old. Write an
inequality to represent at least 70%
of his maximum heart rate.
2. Leia is 38 years old. Write a
compound inequality to represent the
zone between her maximum heart
rate and the upper end of her target
range.
6. s 2 169
5. m 100
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All rights reserved.
117 x 176
3. n 2 121
2
4. a 49
9
2. y 2 81
Heart Rates by Age
There are at least 75 fans at each home
game.
“At least 75” means “75 or more” or “a
number greater than or equal to 75.”
Symbol for “greater than or equal to 75”:
75
Use the chart to answer each question.
N
Z
A
W
Y
F
H
J
S
I
W
E
X
S
E
M
R
N
G
D
M
E
Q
C
D
R
B
G
J
R
F
E
R
U
V
F
K
O
R
E
E
C
S
T
A
M
G
C
L
A
Q
A
O
T
Y
L
N
O
F
M
P
U
T
M
O
U
I
M
J
R
K
H
A
E
P
N
I
T
K
K
T
E
B
L
R
O
E
O
Y
I
L
G
U
G
C
A
U
N
P
V
A
L
U
E
T
D
S
N
M
L
F
E
W
E
R
N
E
E
D
J
K
W
N
J
K
U
O
P
C
S
V
X
1. What is an inequality?
limestone
What kind of stone is the most sour?
a comparison of two unequal values
2. Explain the difference between the symbols and .
The symbol means less than and the symbol means less than or
equal to.
3. Explain the difference between the symbols and .
The symbol means greater than and the symbol means greater
than or equal to.
4. Write , , or to describe the number of students in each
homeroom: There is a limit of 30 students for each homeroom.
30 students
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All rights reserved.
47
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
Holt Mathematics
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
98
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Holt Mathematics
Holt Mathematics