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Solve each inequality. Graph the solution set on
a number line.
1.
ANSWER:
2.
ANSWER:
3. or
ANSWER:
4. or
ANSWER:
5.
ANSWER:
6.
ANSWER:
1-6 Solving Compound and Absolute Value Inequalities
Solve each inequality. Graph the solution set on
7.
a number line.
ANSWER:
1.
ANSWER:
8.
ANSWER:
2.
ANSWER:
9.
ANSWER:
3. or
ANSWER:
10.
4. or ANSWER:
ANSWER:
11. MONEYKhalid is considering several types of paint
for his bedroom. He estimates that he will need
5. between 2 and 3 gallons. The table at the right shows
the price per gallon for each type of paint Khalid is
ANSWER: considering. Write a compound inequality and
determine how much he could be spending.
6.
ANSWER:
ANSWER:
between $43.96 and $77.94
7.
Solve each inequality. Graph the solution set on
ANSWER:
a number line.
12.
ANSWER:
eSolutions Manual - Powered by Cognero Page1
8.
ANSWER:
13.
ANSWER:
9.
ANSWER:
14. or
ANSWER:
10.
ANSWER:
15. or
ANSWER:
11. MONEYKhalid is considering several types of paint
for his bedroom. He estimates that he will need
between 2 and 3 gallons. The table at the right shows
the price per gallon for each type of paint Khalid is
considering. Write a compound inequality and
determine how much he could be spending. 16.
ANSWER:
17.
ANSWER:
ANSWER:
between $43.96 and $77.94
Solve each inequality. Graph the solution set on
18.
a number line.
12.
ANSWER:
ANSWER:
19.
13.
ANSWER:
ANSWER:
14. or
20.
ANSWER:
ANSWER:
15. or
21.
ANSWER:
ANSWER:
16.
ANSWER:
ANATOMYForensic scientists use the equation h
22.
= 2.6f + 47.2 to estimate the height h of a woman
given the length in centimeters f of her femur bone.
a
. Suppose the equation has a margin of error of 3
±
centimeters. Write an inequality to represent the
height of a woman given the length of her femur
17. bone.
ANSWER: b
. If the length of a female skeleton’s femur is 50
centimeters, write and solve an absolute value
inequality that describes the woman’s height in
centimeters.
ANSWER:
18. a.
ANSWER: b.
Write an absolute value inequality for each
graph.
23.
19.
ANSWER:
ANSWER:
24.
ANSWER:
20.
ANSWER:
25.
ANSWER:
26.
21.
ANSWER:
ANSWER:
27.
ANSWER:
ANATOMYForensic scientists use the equation h
22.
= 2.6f + 47.2 to estimate the height h of a woman
given the length in centimeters f of her femur bone.
a 28.
. Suppose the equation has a margin of error of 3
±
centimeters. Write an inequality to represent the
height of a woman given the length of her femur ANSWER:
bone.
b
. If the length of a female skeleton’s femur is 50
centimeters, write and solve an absolute value
inequality that describes the woman s height in 29.
’
centimeters. ANSWER:
ANSWER:
a.
b. 30.
Write an absolute value inequality for each ANSWER:
graph.
23. DOGS The Labrador retriever is one of the most
31.
recognized and popular dogs kept as a pet. Using the
ANSWER: information given, write a compound inequality to
describe the range of healthy weights for a fully
grown female Labrador retriever.
24.
ANSWER:
ANSWER:
25.
ANSWER: GEOMETRY The Exterior Angle Inequality
32.
Theorem states that an exterior angle measure is
greater than the measure of either of its
corresponding remote interior angles. Write two
26. inequalities to express the relationships among the
ANSWER: measures of the angles of ABC.
27.
ANSWER:
ANSWER:
28. Solve each inequality. Graph the solution set on
ANSWER:
a number line.
33.
ANSWER:
29.
ANSWER:
34.
30.
ANSWER:
ANSWER:
DOGS The Labrador retriever is one of the most
31.
recognized and popular dogs kept as a pet. Using the 35.
information given, write a compound inequality to
describe the range of healthy weights for a fully ANSWER:
grown female Labrador retriever.
36.
ANSWER:
ANSWER:
GEOMETRY The Exterior Angle Inequality
32.
Theorem states that an exterior angle measure is
greater than the measure of either of its 37.
corresponding remote interior angles. Write two
inequalities to express the relationships among the ANSWER:
measures of the angles of ABC.
38.
ANSWER:
ANSWER:
Solve each inequality. Graph the solution set on
a number line.
39.
33.
ANSWER:
ANSWER:
34.
40.
ANSWER:
ANSWER:
35.
ANSWER:
Write an algebraic expression to represent
each verbal expression.
41. numbers that are at least 4 units from –5
ANSWER:
36.
ANSWER:
42. numbers that are no more than unit from 1
ANSWER:
37.
ANSWER: numbers that are at least 6 units but no more than 10
43.
units from 2
ANSWER:
38.
AUTO RACINGNASCAR rules stipulate that a
44.
ANSWER: car must conform to a set of 32 templates, each
shaped to fit a different contour of the car. When a
template is placed on a car, the gap between it and
the car cannot exceed the specified tolerance. Each
template is marked on its edge with a colored line
that indicates the tolerance for the template.
39.
ANSWER:
a. Suppose a certain template is 24.42 inches long.
Use the information in the table at the right to write
40. an absolute value inequality for templates with each
line color.
b.
ANSWER: Find the acceptable lengths for that part of a car if
the template has each line color.
c. Graph the solution set for each line color on a
number line.
d
. The tolerance of which line color includes the
tolerances of the other line colors?
Write an algebraic expression to represent Explain your reasoning.
each verbal expression.
numbers that are at least 4 units from 5 ANSWER:
41. – a
.
ANSWER:
b.
numbers that are no more than
42. unit from 1
ANSWER:
c.
43. numbers that are at least 6 units but no more than 10
units from 2
ANSWER:
d. Red; the red line color has the smallest tolerance,
AUTO RACINGNASCAR rules stipulate that a
44. , so the other line colors would be
car must conform to a set of 32 templates, each well within their tolerances.
shaped to fit a different contour of the car. When a
template is placed on a car, the gap between it and Solve each inequality. Graph the solution set on
the car cannot exceed the specified tolerance. Each
template is marked on its edge with a colored line a number line.
that indicates the tolerance for the template. 45.
ANSWER:
46.
a. Suppose a certain template is 24.42 inches long. ANSWER:
Use the information in the table at the right to write
an absolute value inequality for templates with each
line color.
b. Find the acceptable lengths for that part of a car if
the template has each line color. 47.
c. Graph the solution set for each line color on a
number line. ANSWER:
d
. The tolerance of which line color includes the
tolerances of the other line colors?
Explain your reasoning.
ANSWER: 48.
a
.
ANSWER:
b.
49.
c.
ANSWER:
50.
d. Red; the red line color has the smallest tolerance, ANSWER:
, so the other line colors would be
well within their tolerances.
Solve each inequality. Graph the solution set on
a number line. HEALTHHypoglycemia (low blood sugar) and
51.
hyperglycemia (high blood sugar) are potentially
45.
dangerous and occur when a person’s blood sugar
ANSWER: fluctuates by more than 38 mg from the normal blood
sugar level of 88 mg. Write and solve an absolute
value inequality to describe blood sugar levels that
are considered potentially dangerous.
ANSWER:
46.
ANSWER:
AIR TRAVELThe airline on which Drew is flying
52.
has weight restrictions for checked baggage. Drew is
checking one bag.
a. Describe the range of weights that would classify
Drew s bag as free, $25, $50, and unacceptable.
’
47. b
. If Drew s bag weighs 68 pounds, how much will
’
he pay to take it on the plane?
ANSWER:
48.
ANSWER:
ANSWER:
a.
b. $25
49.
ANSWER:
ERROR ANALYSISDavid and Sarah are solving
53.
. Is either of them
correct? Explain your reasoning.
50.
ANSWER:
ANSWER:
Sample answer: David; when Sarah converted the
absolute value into two inequalities, she mistakenly
switched
HEALTHHypoglycemia (low blood sugar) and
51. the inequality symbols.
hyperglycemia (high blood sugar) are potentially
dangerous and occur when a person’s blood sugar
CHALLENGESolve
fluctuates by more than 38 mg from the normal blood 54.
sugar level of 88 mg. Write and solve an absolute ANSWER:
value inequality to describe blood sugar levels that x < 0
are considered potentially dangerous.
REASONING Determine whether each
ANSWER:
statement is true or false. If false, provide a
counterexample.
55. The graph of a compound inequality involving an and
statement is bounded on the left and right by two
AIR TRAVELThe airline on which Drew is flying
52. values of x.
has weight restrictions for checked baggage. Drew is
checking one bag.
a. Describe the range of weights that would classify ANSWER:
Drew s bag as free, $25, $50, and unacceptable. False; sample answer: the graph of
’ x > 2 and x > 5 is a ray bounded only on one end.
b
. If Drew s bag weighs 68 pounds, how much will
’
he pay to take it on the plane?
56. The graph of a compound inequality involving an or
statement contains a region of values that are not
solutions.
ANSWER:
False; sample answer: the graph of
x > 2 or x < 3 includes the entire number line.
57. The graph of a compound inequality involving an and
statement includes values that make all parts of the
given statement true.
ANSWER:
a. ANSWER:
b. $25 True
WRITING IN MATHAn alternate definition of
58.
ERROR ANALYSISDavid and Sarah are solving
53.
. Is either of them absolute value is to define as the distance
correct? Explain your reasoning. between a and b on the number line. Explain how
this definition can be used to solve inequalities of the
form .
ANSWER:
Sample answer:
represents
the distance between some unknown value of the
ANSWER: variable x and a point c on the number line. The
Sample answer: David; when Sarah converted the solution set of the inequality is the set of all numbers
absolute value into two inequalities, she mistakenly such that the distance from the numbers to c is less
switched than r units. Use a number line to find the numbers
the inequality symbols. that are r units from c in either direction.
CHALLENGESolve
54.
REASONINGThe graphs of the solutions of two
59.
different absolute value inequalities are shown.
ANSWER: Compare and contrast the absolute value inequalities.
x < 0
REASONING Determine whether each
statement is true or false. If false, provide a
counterexample.
The graph of a compound inequality involving an and ANSWER:
55.
statement is bounded on the left and right by two Sample answer: The graph on the left indicates a
solution set from 3 to 5. The
values of x. –
graph on the right indicates a solution
ANSWER: set of all numbers less than or equal to
False; sample answer: the graph of 3 or greater than or equal to 5.
–
x > 2 and x > 5 is a ray bounded only on one end.
OPEN ENDED
60. Write an absolute value inequality
The graph of a compound inequality involving an or with a solution of
56.
statement contains a region of values that are not
solutions. ANSWER:
Sample answer:
ANSWER:
False; sample answer: the graph of
x > 2 or x < 3 includes the entire number line.
WHICH ONE DOESNT BELONG?
’ Identify the
The graph of a compound inequality involving an and 61.
57. compound inequality that is not the same as the other
statement includes values that make all parts of the three. Explain your reasoning.
given statement true.
ANSWER:
True
ANSWER:
WRITING IN MATHAn alternate definition of
58.
absolute value is to define as the distance Each of these has a non-empty solution set except
between a and b on the number line. Explain how for x > 5 and x < 1. There are no values of x that are
this definition can be used to solve inequalities of the simultaneously greater than 5 and less than 1.
form .
WRITING IN MATHSummarize the difference
62.
between and compound inequalities and or
ANSWER: compound inequalities.
Sample answer:
represents
the distance between some unknown value of the ANSWER:
variable x and a point c on the number line. The Sample answer: A compound inequality that contains
solution set of the inequality is the set of all numbers and is true if and only if both individual inequalities
such that the distance from the numbers to c is less are true, while an inequality containing or only needs
than r units. Use a number line to find the numbers one of the individual inequalities to be true.
that are r units from c in either direction. Which of the following best describes the graph of
63.
the equations below?
REASONINGThe graphs of the solutions of two
59.
different absolute value inequalities are shown.
Compare and contrast the absolute value inequalities.
A The lines have the same x-intercept.
B The lines have the same y-intercept.
C The lines are parallel.
D The lines are perpendicular.
ANSWER:
Sample answer: The graph on the left indicates a ANSWER:
C
solution set from 3 to 5. The
–
graph on the right indicates a solution SAT/ACT Find an expression equivalent
set of all numbers less than or equal to 64.
3 or greater than or equal to 5.
– to
OPEN ENDED
60. Write an absolute value inequality
with a solution of
F
ANSWER:
Sample answer:
G
H
WHICH ONE DOESNT BELONG?
’ Identify the
61.
compound inequality that is not the same as the other J
three. Explain your reasoning.
K
ANSWER:
Each of these has a non-empty solution set except ANSWER:
for x > 5 and x < 1. There are no values of x that are K
simultaneously greater than 5 and less than 1.
GRIDDED RESPONSEHow many cubes that
65.
measure 4 centimeters on each side can be placed
WRITING IN MATHSummarize the difference
62. completely inside the box below?
between and compound inequalities and or
compound inequalities.
ANSWER:
Sample answer: A compound inequality that contains
and is true if and only if both individual inequalities
are true, while an inequality containing or only needs
one of the individual inequalities to be true. ANSWER:
60
63. Which of the following best describes the graph of Which graph represents the solution set for
the equations below? 66.
A The lines have the same x-intercept. A
B The lines have the same y-intercept.
B
C The lines are parallel.
D The lines are perpendicular. C
D
ANSWER:
C
ANSWER:
SAT/ACT Find an expression equivalent A
64.
HEALTHThe National Heart Association
to 67.
recommends that less than 30% of a person’s total
daily caloric intake come from fat. One gram of fat
yields nine Calories. Consider a healthy 21-year-old
F
whose average caloric intake is between 2500 and
3300 Calories.
a
. Write an inequality that represents the suggested
G fat intake for the person.
b
H . What is the greatest suggested fat intake for the
person?
ANSWER:
J a.
b.110g
K TRAVEL Maggie is planning a 5-day trip to a family
68.
reunion. She wants to spend no more than $1000.
Her plane ticket is $375, and the hotel is $85 per
night.
ANSWER:
a
K . Let f represent the cost of food for one day. Write
an inequality to represent this situation.
b
GRIDDED RESPONSEHow many cubes that . Solve the inequality and interpret the solution.
65.
measure 4 centimeters on each side can be placed
completely inside the box below? ANSWER:
a.
b. She can spend no more than $40 per day on food.
Solve each equation. Check your solutions.
69.
ANSWER:
ANSWER:
60
66. Which graph represents the solution set for
70.
A ANSWER:
B
C
71.
D
ANSWER:
ANSWER:
A
Name the property illustrated by each
HEALTHThe National Heart Association
67.
recommends that less than 30% of a person s total statement.
’ If then
daily caloric intake come from fat. One gram of fat 72.
yields nine Calories. Consider a healthy 21-year-old ANSWER:
whose average caloric intake is between 2500 and Addition (=)
3300 Calories.
a
. Write an inequality that represents the suggested
fat intake for the person. 73. If and then
b
. What is the greatest suggested fat intake for the
person?
ANSWER:
Transitive (=)
ANSWER:
a. If
b.110g 74. then
TRAVEL Maggie is planning a 5-day trip to a family ANSWER:
68. Assoc. (+)
reunion. She wants to spend no more than $1000.
Her plane ticket is $375, and the hotel is $85 per
night.
a
. Let f represent the cost of food for one day. Write
an inequality to represent this situation.
b
. Solve the inequality and interpret the solution.
ANSWER:
a.
b. She can spend no more than $40 per day on food.
Solve each equation. Check your solutions.
69.
ANSWER:
70.
ANSWER:
71.
ANSWER:
Name the property illustrated by each
statement.
72. If then
ANSWER:
Addition (=)
73. If and then
ANSWER:
Transitive (=)
74. If then
ANSWER:
Assoc. (+)
Solve each inequality. Graph the solution set on
a number line.
1.
ANSWER:
2.
ANSWER:
3. or
ANSWER:
4. or
ANSWER:
5.
ANSWER:
6.
ANSWER:
7.
Solve each inequality. Graph the solution set on
a number line.
ANSWER:
1.
ANSWER:
8.
ANSWER:
2.
ANSWER:
9.
ANSWER:
3. or
ANSWER:
10.
ANSWER:
4. or
ANSWER:
11. MONEYKhalid is considering several types of paint
for his bedroom. He estimates that he will need
between 2 and 3 gallons. The table at the right shows
5. the price per gallon for each type of paint Khalid is
considering. Write a compound inequality and
ANSWER: determine how much he could be spending.
6.
ANSWER:
ANSWER:
between $43.96 and $77.94
7.
Solve each inequality. Graph the solution set on
ANSWER:
a number line.
12.
ANSWER:
8.
ANSWER:
13.
ANSWER:
9.
ANSWER:
14. or
ANSWER:
10.
ANSWER:
15. or
ANSWER:
11. MONEYKhalid is considering several types of paint
for his bedroom. He estimates that he will need
between 2 and 3 gallons. The table at the right shows
the price per gallon for each type of paint Khalid is
considering. Write a compound inequality and 16.
determine how much he could be spending.
ANSWER:
17.
ANSWER:
ANSWER:
1-6 Solving Compound and Absolute Value Inequalities
between $43.96 and $77.94
Solve each inequality. Graph the solution set on
18.
a number line.
ANSWER:
12.
ANSWER:
19.
13.
ANSWER:
ANSWER:
14. or 20.
ANSWER:
ANSWER:
15. or
21.
ANSWER:
ANSWER:
16.
ANATOMYForensic scientists use the equation h
22.
ANSWER: = 2.6f + 47.2 to estimate the height h of a woman
given the length in centimeters f of her femur bone.
a
. Suppose the equation has a margin of error of 3
±
centimeters. Write an inequality to represent the
height of a woman given the length of her femur
17. bone.
b
. If the length of a female skeleton’s femur is 50
ANSWER: centimeters, write and solve an absolute value
inequality that describes the woman s height in
’
centimeters.
ANSWER:
18. a.
b.
ANSWER:
Write an absolute value inequality for each
graph.
eSolutions Manual - Powered by Cognero Page2
23.
ANSWER:
19.
ANSWER:
24.
ANSWER:
20.
ANSWER:
25.
ANSWER:
26.
21.
ANSWER:
ANSWER:
27.
ANSWER:
ANATOMYForensic scientists use the equation h
22.
= 2.6f + 47.2 to estimate the height h of a woman
given the length in centimeters f of her femur bone.
a 28.
. Suppose the equation has a margin of error of 3
±
centimeters. Write an inequality to represent the ANSWER:
height of a woman given the length of her femur
bone.
b
. If the length of a female skeleton’s femur is 50
centimeters, write and solve an absolute value 29.
inequality that describes the woman’s height in
centimeters. ANSWER:
ANSWER:
a.
b. 30.
ANSWER:
Write an absolute value inequality for each
graph.
DOGS The Labrador retriever is one of the most
31.
23. recognized and popular dogs kept as a pet. Using the
information given, write a compound inequality to
ANSWER: describe the range of healthy weights for a fully
grown female Labrador retriever.
24.
ANSWER:
ANSWER:
25.
ANSWER: GEOMETRY The Exterior Angle Inequality
32.
Theorem states that an exterior angle measure is
greater than the measure of either of its
corresponding remote interior angles. Write two
26. inequalities to express the relationships among the
measures of the angles of ABC.
ANSWER:
27.
ANSWER:
ANSWER:
28. Solve each inequality. Graph the solution set on
a number line.
ANSWER:
33.
ANSWER:
29.
ANSWER:
34.
30.
ANSWER:
ANSWER:
DOGS The Labrador retriever is one of the most
31.
recognized and popular dogs kept as a pet. Using the 35.
information given, write a compound inequality to ANSWER:
describe the range of healthy weights for a fully
grown female Labrador retriever.
36.
ANSWER:
ANSWER:
GEOMETRYThe Exterior Angle Inequality
32.
Theorem states that an exterior angle measure is 37.
greater than the measure of either of its
corresponding remote interior angles. Write two ANSWER:
inequalities to express the relationships among the
measures of the angles of ABC.
38.
ANSWER:
ANSWER:
Solve each inequality. Graph the solution set on
a number line.
39.
33.
ANSWER:
ANSWER:
34.
40.
ANSWER:
ANSWER:
35.
ANSWER: Write an algebraic expression to represent
each verbal expression.
41. numbers that are at least 4 units from –5
ANSWER:
36.
ANSWER:
numbers that are no more than
42. unit from 1
ANSWER:
37.
43. numbers that are at least 6 units but no more than 10
ANSWER: units from 2
ANSWER:
38.
AUTO RACINGNASCAR rules stipulate that a
44.
car must conform to a set of 32 templates, each
ANSWER: shaped to fit a different contour of the car. When a
template is placed on a car, the gap between it and
the car cannot exceed the specified tolerance. Each
template is marked on its edge with a colored line
that indicates the tolerance for the template.
39.
ANSWER:
a. Suppose a certain template is 24.42 inches long.
Use the information in the table at the right to write
an absolute value inequality for templates with each
40. line color.
b. Find the acceptable lengths for that part of a car if
ANSWER: the template has each line color.
c. Graph the solution set for each line color on a
number line.
d
. The tolerance of which line color includes the
tolerances of the other line colors?
Write an algebraic expression to represent Explain your reasoning.
ANSWER:
each verbal expression.
41. numbers that are at least 4 units from –5 a
.
ANSWER:
b.
numbers that are no more than
42. unit from 1
c.
ANSWER:
43. numbers that are at least 6 units but no more than 10
units from 2
ANSWER:
d. Red; the red line color has the smallest tolerance,
, so the other line colors would be
AUTO RACINGNASCAR rules stipulate that a
44. well within their tolerances.
car must conform to a set of 32 templates, each
shaped to fit a different contour of the car. When a Solve each inequality. Graph the solution set on
template is placed on a car, the gap between it and
the car cannot exceed the specified tolerance. Each a number line.
template is marked on its edge with a colored line 45.
that indicates the tolerance for the template.
ANSWER:
46.
a. Suppose a certain template is 24.42 inches long. ANSWER:
Use the information in the table at the right to write
an absolute value inequality for templates with each
line color.
b. Find the acceptable lengths for that part of a car if
the template has each line color. 47.
c. Graph the solution set for each line color on a ANSWER:
number line.
d
. The tolerance of which line color includes the
tolerances of the other line colors?
Explain your reasoning.
48.
ANSWER:
a ANSWER:
.
b.
49.
c.
ANSWER:
50.
ANSWER:
d. Red; the red line color has the smallest tolerance,
, so the other line colors would be
well within their tolerances.
Solve each inequality. Graph the solution set on
HEALTHHypoglycemia (low blood sugar) and
51.
a number line. hyperglycemia (high blood sugar) are potentially
45. dangerous and occur when a person s blood sugar
’
fluctuates by more than 38 mg from the normal blood
ANSWER: sugar level of 88 mg. Write and solve an absolute
value inequality to describe blood sugar levels that
are considered potentially dangerous.
ANSWER:
46.
ANSWER:
AIR TRAVELThe airline on which Drew is flying
52.
has weight restrictions for checked baggage. Drew is
checking one bag.
a. Describe the range of weights that would classify
Drew s bag as free, $25, $50, and unacceptable.
’
47. b
. If Drew s bag weighs 68 pounds, how much will
’
he pay to take it on the plane?
ANSWER:
48.
ANSWER:
ANSWER:
a.
b. $25
49.
ERROR ANALYSISDavid and Sarah are solving
53.
ANSWER: . Is either of them
correct? Explain your reasoning.
50.
ANSWER:
ANSWER:
Sample answer: David; when Sarah converted the
absolute value into two inequalities, she mistakenly
switched
the inequality symbols.
HEALTHHypoglycemia (low blood sugar) and
51.
hyperglycemia (high blood sugar) are potentially
CHALLENGESolve
dangerous and occur when a person s blood sugar 54.
’
fluctuates by more than 38 mg from the normal blood
sugar level of 88 mg. Write and solve an absolute ANSWER:
value inequality to describe blood sugar levels that x < 0
are considered potentially dangerous. REASONING Determine whether each
statement is true or false. If false, provide a
ANSWER:
counterexample.
55. The graph of a compound inequality involving an and
statement is bounded on the left and right by two
AIR TRAVELThe airline on which Drew is flying
52. values of x.
has weight restrictions for checked baggage. Drew is
checking one bag. ANSWER:
a. Describe the range of weights that would classify False; sample answer: the graph of
Drew s bag as free, $25, $50, and unacceptable. x > 2 and x > 5 is a ray bounded only on one end.
’
b
. If Drew s bag weighs 68 pounds, how much will
’
he pay to take it on the plane? The graph of a compound inequality involving an or
56.
statement contains a region of values that are not
solutions.
ANSWER:
False; sample answer: the graph of
x > 2 or x < 3 includes the entire number line.
57. The graph of a compound inequality involving an and
statement includes values that make all parts of the
given statement true.
ANSWER:
a. ANSWER:
b. $25 True
WRITING IN MATHAn alternate definition of
58.
ERROR ANALYSISDavid and Sarah are solving
53. absolute value is to define as the distance
. Is either of them between a and b on the number line. Explain how
correct? Explain your reasoning. this definition can be used to solve inequalities of the
form .
ANSWER:
Sample answer:
represents
the distance between some unknown value of the
variable x and a point c on the number line. The
ANSWER: solution set of the inequality is the set of all numbers
Sample answer: David; when Sarah converted the such that the distance from the numbers to c is less
absolute value into two inequalities, she mistakenly than r units. Use a number line to find the numbers
switched that are r units from c in either direction.
the inequality symbols.
REASONINGThe graphs of the solutions of two
59.
CHALLENGESolve
54. different absolute value inequalities are shown.
Compare and contrast the absolute value inequalities.
ANSWER:
x < 0
REASONING Determine whether each
statement is true or false. If false, provide a
counterexample.
The graph of a compound inequality involving an and ANSWER:
55. Sample answer: The graph on the left indicates a
statement is bounded on the left and right by two solution set from 3 to 5. The
values of x. –
graph on the right indicates a solution
set of all numbers less than or equal to
ANSWER: 3 or greater than or equal to 5.
False; sample answer: the graph of –
x > 2 and x > 5 is a ray bounded only on one end.
OPEN ENDED
60. Write an absolute value inequality
The graph of a compound inequality involving an or with a solution of
56.
statement contains a region of values that are not ANSWER:
solutions. Sample answer:
ANSWER:
False; sample answer: the graph of
x > 2 or x < 3 includes the entire number line.
WHICH ONE DOESNT BELONG?
’ Identify the
61.
The graph of a compound inequality involving an and compound inequality that is not the same as the other
57. three. Explain your reasoning.
statement includes values that make all parts of the
given statement true.
ANSWER:
True
ANSWER:
WRITING IN MATHAn alternate definition of
58. Each of these has a non-empty solution set except
absolute value is to define as the distance for x > 5 and x < 1. There are no values of x that are
between a and b on the number line. Explain how simultaneously greater than 5 and less than 1.
this definition can be used to solve inequalities of the
WRITING IN MATHSummarize the difference
form . 62.
between and compound inequalities and or
compound inequalities.
ANSWER:
Sample answer:
represents
ANSWER:
the distance between some unknown value of the Sample answer: A compound inequality that contains
variable x and a point c on the number line. The and is true if and only if both individual inequalities
solution set of the inequality is the set of all numbers are true, while an inequality containing or only needs
such that the distance from the numbers to c is less one of the individual inequalities to be true.
than r units. Use a number line to find the numbers
that are r units from c in either direction. 63. Which of the following best describes the graph of
the equations below?
REASONINGThe graphs of the solutions of two
59.
different absolute value inequalities are shown.
Compare and contrast the absolute value inequalities. A The lines have the same x-intercept.
B The lines have the same y-intercept.
C The lines are parallel.
D The lines are perpendicular.
ANSWER:
ANSWER:
C
Sample answer: The graph on the left indicates a
solution set from 3 to 5. The
– SAT/ACT Find an expression equivalent
graph on the right indicates a solution 64.
set of all numbers less than or equal to
3 or greater than or equal to 5. to
–
OPEN ENDED
60. Write an absolute value inequality
F
with a solution of
ANSWER:
Sample answer: G
H
WHICH ONE DOESNT BELONG?
’ Identify the
61. J
compound inequality that is not the same as the other
three. Explain your reasoning.
K
ANSWER:
ANSWER: K
Each of these has a non-empty solution set except
for x > 5 and x < 1. There are no values of x that are
GRIDDED RESPONSEHow many cubes that
simultaneously greater than 5 and less than 1. 65.
measure 4 centimeters on each side can be placed
completely inside the box below?
WRITING IN MATHSummarize the difference
62.
between and compound inequalities and or
compound inequalities.
ANSWER:
Sample answer: A compound inequality that contains
and is true if and only if both individual inequalities
are true, while an inequality containing or only needs ANSWER:
one of the individual inequalities to be true. 60
63. Which of the following best describes the graph of 66. Which graph represents the solution set for
the equations below?
A
A The lines have the same x-intercept.
B The lines have the same y-intercept. B
C The lines are parallel.
D The lines are perpendicular. C
D
ANSWER:
C ANSWER:
A
SAT/ACT Find an expression equivalent
64.
HEALTHThe National Heart Association
67.
to recommends that less than 30% of a person’s total
daily caloric intake come from fat. One gram of fat
yields nine Calories. Consider a healthy 21-year-old
whose average caloric intake is between 2500 and
F
3300 Calories.
a
. Write an inequality that represents the suggested
fat intake for the person.
G
b
. What is the greatest suggested fat intake for the
H person?
ANSWER:
J a.
b.110g
TRAVEL Maggie is planning a 5-day trip to a family
K 68.
reunion. She wants to spend no more than $1000.
Her plane ticket is $375, and the hotel is $85 per
night.
ANSWER: a
K . Let f represent the cost of food for one day. Write
an inequality to represent this situation.
b
. Solve the inequality and interpret the solution.
GRIDDED RESPONSEHow many cubes that
65.
measure 4 centimeters on each side can be placed ANSWER:
completely inside the box below? a.
b. She can spend no more than $40 per day on food.
Solve each equation. Check your solutions.
69.
ANSWER:
ANSWER:
60
66. Which graph represents the solution set for
70.
A ANSWER:
B
71.
C
D
ANSWER:
ANSWER:
A Name the property illustrated by each
statement.
HEALTHThe National Heart Association
67. If then
recommends that less than 30% of a person s total 72.
’
daily caloric intake come from fat. One gram of fat
yields nine Calories. Consider a healthy 21-year-old ANSWER:
whose average caloric intake is between 2500 and Addition (=)
3300 Calories.
a 73. If and then
. Write an inequality that represents the suggested
fat intake for the person.
b
. What is the greatest suggested fat intake for the
person? ANSWER:
Transitive (=)
ANSWER:
a. If
74. then
b.110g
ANSWER:
TRAVELMaggie is planning a 5-day trip to a family
68. Assoc. (+)
reunion. She wants to spend no more than $1000.
Her plane ticket is $375, and the hotel is $85 per
night.
a
. Let f represent the cost of food for one day. Write
an inequality to represent this situation.
b
. Solve the inequality and interpret the solution.
ANSWER:
a.
b. She can spend no more than $40 per day on food.
Solve each equation. Check your solutions.
69.
ANSWER:
70.
ANSWER:
71.
ANSWER:
Name the property illustrated by each
statement.
72. If then
ANSWER:
Addition (=)
73. If and then
ANSWER:
Transitive (=)
74. If then
ANSWER:
Assoc. (+)
Solve each inequality. Graph the solution set on
a number line.
1.
ANSWER:
2.
ANSWER:
3. or
ANSWER:
4. or
ANSWER:
5.
ANSWER:
6.
ANSWER:
7.
ANSWER:
Solve each inequality. Graph the solution set on
a number line.
1.
ANSWER:
8.
ANSWER:
2.
9.
ANSWER:
ANSWER:
3. or
ANSWER:
10.
ANSWER:
4. or
ANSWER:
11. MONEYKhalid is considering several types of paint
for his bedroom. He estimates that he will need
between 2 and 3 gallons. The table at the right shows
the price per gallon for each type of paint Khalid is
considering. Write a compound inequality and
5. determine how much he could be spending.
ANSWER:
6.
ANSWER:
ANSWER:
between $43.96 and $77.94
Solve each inequality. Graph the solution set on
a number line.
7.
12.
ANSWER:
ANSWER:
8.
13.
ANSWER:
ANSWER:
9.
14. or
ANSWER:
ANSWER:
10.
15. or
ANSWER:
ANSWER:
11. MONEYKhalid is considering several types of paint
for his bedroom. He estimates that he will need
between 2 and 3 gallons. The table at the right shows 16.
the price per gallon for each type of paint Khalid is ANSWER:
considering. Write a compound inequality and
determine how much he could be spending.
17.
ANSWER:
ANSWER:
between $43.96 and $77.94 18.
Solve each inequality. Graph the solution set on ANSWER:
a number line.
12.
ANSWER:
19.
ANSWER:
13.
ANSWER:
20.
14. or ANSWER:
ANSWER:
21.
15. or ANSWER:
ANSWER:
ANATOMYForensic scientists use the equation h
22.
16. = 2.6f + 47.2 to estimate the height h of a woman
given the length in centimeters f of her femur bone.
ANSWER: a
. Suppose the equation has a margin of error of 3
±
centimeters. Write an inequality to represent the
height of a woman given the length of her femur
bone.
b
. If the length of a female skeleton’s femur is 50
17. centimeters, write and solve an absolute value
inequality that describes the woman’s height in
ANSWER: centimeters.
ANSWER:
a.
b.
18.
Write an absolute value inequality for each
ANSWER: graph.
23.
ANSWER:
19.
ANSWER:
24.
ANSWER:
25.
20.
ANSWER:
ANSWER:
26.
ANSWER:
21.
ANSWER:
27.
ANSWER:
ANATOMYForensic scientists use the equation h
22. 28.
= 2.6f + 47.2 to estimate the height h of a woman
given the length in centimeters f of her femur bone. ANSWER:
a
. Suppose the equation has a margin of error of 3
±
centimeters. Write an inequality to represent the
height of a woman given the length of her femur
bone. 29.
b
. If the length of a female skeleton’s femur is 50
ANSWER:
centimeters, write and solve an absolute value
inequality that describes the woman’s height in
centimeters.
30.
ANSWER:
a.
1-6 Solving Compound and Absolute Value Inequalities ANSWER:
b.
Write an absolute value inequality for each DOGS The Labrador retriever is one of the most
graph. 31.
recognized and popular dogs kept as a pet. Using the
information given, write a compound inequality to
23. describe the range of healthy weights for a fully
grown female Labrador retriever.
ANSWER:
24.
ANSWER:
ANSWER:
GEOMETRY The Exterior Angle Inequality
32.
25. Theorem states that an exterior angle measure is
ANSWER: greater than the measure of either of its
corresponding remote interior angles. Write two
inequalities to express the relationships among the
measures of the angles of ABC.
26.
ANSWER:
27.
ANSWER:
ANSWER:
Solve each inequality. Graph the solution set on
a number line.
28.
33.
ANSWER:
ANSWER:
29.
ANSWER:
34.
ANSWER:
30.
ANSWER:
35.
DOGS The Labrador retriever is one of the most ANSWER:
31.
recognized and popular dogs kept as a pet. Using the
information given, write a compound inequality to
describe the range of healthy weights for a fully
eSolutions Manual - Powered by Cognero Page3
grown female Labrador retriever.
36.
ANSWER:
ANSWER:
37.
GEOMETRY The Exterior Angle Inequality
32.
Theorem states that an exterior angle measure is ANSWER:
greater than the measure of either of its
corresponding remote interior angles. Write two
inequalities to express the relationships among the
measures of the angles of ABC.
38.
ANSWER:
ANSWER:
39.
Solve each inequality. Graph the solution set on
a number line.
ANSWER:
33.
ANSWER:
40.
34.
ANSWER:
ANSWER:
35. Write an algebraic expression to represent
each verbal expression.
ANSWER: numbers that are at least 4 units from 5
41. –
ANSWER:
36.
42. numbers that are no more than unit from 1
ANSWER:
ANSWER:
43. numbers that are at least 6 units but no more than 10
37. units from 2
ANSWER:
ANSWER:
AUTO RACINGNASCAR rules stipulate that a
44.
car must conform to a set of 32 templates, each
38. shaped to fit a different contour of the car. When a
template is placed on a car, the gap between it and
ANSWER: the car cannot exceed the specified tolerance. Each
template is marked on its edge with a colored line
that indicates the tolerance for the template.
39.
ANSWER:
a. Suppose a certain template is 24.42 inches long.
Use the information in the table at the right to write
an absolute value inequality for templates with each
line color.
b. Find the acceptable lengths for that part of a car if
40. the template has each line color.
c. Graph the solution set for each line color on a
ANSWER: number line.
d
. The tolerance of which line color includes the
tolerances of the other line colors?
Explain your reasoning.
ANSWER:
Write an algebraic expression to represent a
.
each verbal expression.
numbers that are at least 4 units from 5
41. –
ANSWER: b.
numbers that are no more than c.
42. unit from 1
ANSWER:
43. numbers that are at least 6 units but no more than 10
units from 2
ANSWER: d. Red; the red line color has the smallest tolerance,
, so the other line colors would be
well within their tolerances.
AUTO RACINGNASCAR rules stipulate that a
44. Solve each inequality. Graph the solution set on
car must conform to a set of 32 templates, each
shaped to fit a different contour of the car. When a a number line.
template is placed on a car, the gap between it and 45.
the car cannot exceed the specified tolerance. Each
template is marked on its edge with a colored line ANSWER:
that indicates the tolerance for the template.
46.
ANSWER:
a. Suppose a certain template is 24.42 inches long.
Use the information in the table at the right to write
an absolute value inequality for templates with each
line color. 47.
b. Find the acceptable lengths for that part of a car if ANSWER:
the template has each line color.
c. Graph the solution set for each line color on a
number line.
d
. The tolerance of which line color includes the
tolerances of the other line colors? 48.
Explain your reasoning.
ANSWER:
ANSWER:
a
.
b.
49.
ANSWER:
c.
50.
ANSWER:
d. Red; the red line color has the smallest tolerance,
, so the other line colors would be
well within their tolerances.
HEALTHHypoglycemia (low blood sugar) and
51.
Solve each inequality. Graph the solution set on hyperglycemia (high blood sugar) are potentially
dangerous and occur when a person’s blood sugar
a number line. fluctuates by more than 38 mg from the normal blood
45. sugar level of 88 mg. Write and solve an absolute
value inequality to describe blood sugar levels that
ANSWER: are considered potentially dangerous.
ANSWER:
AIR TRAVELThe airline on which Drew is flying
52.
46. has weight restrictions for checked baggage. Drew is
checking one bag.
ANSWER:
a. Describe the range of weights that would classify
Drew s bag as free, $25, $50, and unacceptable.
’
b
. If Drew s bag weighs 68 pounds, how much will
’
he pay to take it on the plane?
47.
ANSWER:
48.
ANSWER:
ANSWER:
a.
b. $25
53. ERROR ANALYSISDavid and Sarah are solving
49. . Is either of them
correct? Explain your reasoning.
ANSWER:
50.
ANSWER:
Sample answer: David; when Sarah converted the
ANSWER: absolute value into two inequalities, she mistakenly
switched
the inequality symbols.
54. CHALLENGESolve
HEALTHHypoglycemia (low blood sugar) and
51.
hyperglycemia (high blood sugar) are potentially
dangerous and occur when a person s blood sugar ANSWER:
’ x < 0
fluctuates by more than 38 mg from the normal blood
sugar level of 88 mg. Write and solve an absolute REASONING Determine whether each
value inequality to describe blood sugar levels that
are considered potentially dangerous. statement is true or false. If false, provide a
counterexample.
55. The graph of a compound inequality involving an and
ANSWER: statement is bounded on the left and right by two
values of x.
ANSWER:
AIR TRAVELThe airline on which Drew is flying
52. False; sample answer: the graph of
has weight restrictions for checked baggage. Drew is x > 2 and x > 5 is a ray bounded only on one end.
checking one bag.
a. Describe the range of weights that would classify
Drew s bag as free, $25, $50, and unacceptable.
’ 56. The graph of a compound inequality involving an or
b
. If Drew s bag weighs 68 pounds, how much will
’ statement contains a region of values that are not
he pay to take it on the plane? solutions.
ANSWER:
False; sample answer: the graph of
x > 2 or x < 3 includes the entire number line.
57. The graph of a compound inequality involving an and
statement includes values that make all parts of the
given statement true.
ANSWER:
True
ANSWER:
a.
58. WRITING IN MATHAn alternate definition of
b. $25 absolute value is to define as the distance
between a and b on the number line. Explain how
53. ERROR ANALYSISDavid and Sarah are solving this definition can be used to solve inequalities of the
. Is either of them form .
correct? Explain your reasoning.
ANSWER:
Sample answer: represents
the distance between some unknown value of the
variable x and a point c on the number line. The
solution set of the inequality is the set of all numbers
such that the distance from the numbers to c is less
ANSWER: than r units. Use a number line to find the numbers
Sample answer: David; when Sarah converted the that are r units from c in either direction.
absolute value into two inequalities, she mistakenly
switched
the inequality symbols. 59. REASONINGThe graphs of the solutions of two
different absolute value inequalities are shown.
Compare and contrast the absolute value inequalities.
54. CHALLENGESolve
ANSWER:
x < 0
REASONING Determine whether each ANSWER:
statement is true or false. If false, provide a Sample answer: The graph on the left indicates a
counterexample. solution set from 3 to 5. The
The graph of a compound inequality involving an and –
55. graph on the right indicates a solution
statement is bounded on the left and right by two set of all numbers less than or equal to
values of x. 3 or greater than or equal to 5.
–
ANSWER:
OPEN ENDED
False; sample answer: the graph of 60. Write an absolute value inequality
x > 2 and x > 5 is a ray bounded only on one end. with a solution of
ANSWER:
The graph of a compound inequality involving an or Sample answer:
56.
statement contains a region of values that are not
solutions.
ANSWER:
WHICH ONE DOESNT BELONG?
’ Identify the
False; sample answer: the graph of 61.
x > 2 or x < 3 includes the entire number line. compound inequality that is not the same as the other
three. Explain your reasoning.
57. The graph of a compound inequality involving an and
statement includes values that make all parts of the
given statement true.
ANSWER:
ANSWER:
True Each of these has a non-empty solution set except
for x > 5 and x < 1. There are no values of x that are
WRITING IN MATHAn alternate definition of
58. simultaneously greater than 5 and less than 1.
absolute value is to define as the distance
WRITING IN MATHSummarize the difference
between a and b on the number line. Explain how 62.
this definition can be used to solve inequalities of the between and compound inequalities and or
form . compound inequalities.
ANSWER:
ANSWER: Sample answer: A compound inequality that contains
Sample answer:
represents and is true if and only if both individual inequalities
the distance between some unknown value of the are true, while an inequality containing or only needs
variable x and a point c on the number line. The one of the individual inequalities to be true.
solution set of the inequality is the set of all numbers Which of the following best describes the graph of
such that the distance from the numbers to c is less 63.
than r units. Use a number line to find the numbers the equations below?
that are r units from c in either direction.
REASONINGThe graphs of the solutions of two
59. A The lines have the same x-intercept.
different absolute value inequalities are shown. B The lines have the same y-intercept.
Compare and contrast the absolute value inequalities. C The lines are parallel.
D The lines are perpendicular.
ANSWER:
C
ANSWER: SAT/ACT Find an expression equivalent
Sample answer: The graph on the left indicates a 64.
solution set from 3 to 5. The
– to
graph on the right indicates a solution
set of all numbers less than or equal to
3 or greater than or equal to 5.
–
F
OPEN ENDED
60. Write an absolute value inequality
with a solution of
G
ANSWER:
Sample answer: H
J
WHICH ONE DOESNT BELONG?
’ Identify the
61.
compound inequality that is not the same as the other K
three. Explain your reasoning.
ANSWER:
K
ANSWER:
GRIDDED RESPONSEHow many cubes that
Each of these has a non-empty solution set except 65.
for x > 5 and x < 1. There are no values of x that are measure 4 centimeters on each side can be placed
simultaneously greater than 5 and less than 1. completely inside the box below?
WRITING IN MATHSummarize the difference
62.
between and compound inequalities and or
compound inequalities.
ANSWER:
Sample answer: A compound inequality that contains ANSWER:
and is true if and only if both individual inequalities 60
are true, while an inequality containing or only needs Which graph represents the solution set for
one of the individual inequalities to be true. 66.
63. Which of the following best describes the graph of
the equations below? A
B
A The lines have the same x-intercept.
B The lines have the same y-intercept. C
C The lines are parallel. D
D The lines are perpendicular.
ANSWER:
A
ANSWER:
C
HEALTHThe National Heart Association
67.
SAT/ACT Find an expression equivalent recommends that less than 30% of a person’s total
64. daily caloric intake come from fat. One gram of fat
yields nine Calories. Consider a healthy 21-year-old
to whose average caloric intake is between 2500 and
3300 Calories.
a
. Write an inequality that represents the suggested
F
fat intake for the person.
b
. What is the greatest suggested fat intake for the
person?
G
ANSWER:
H a.
b.110g
J TRAVEL Maggie is planning a 5-day trip to a family
68.
reunion. She wants to spend no more than $1000.
K Her plane ticket is $375, and the hotel is $85 per
night.
a
. Let f represent the cost of food for one day. Write
an inequality to represent this situation.
ANSWER: b
. Solve the inequality and interpret the solution.
K
ANSWER:
GRIDDED RESPONSEHow many cubes that a.
65.
measure 4 centimeters on each side can be placed b. She can spend no more than $40 per day on food.
completely inside the box below?
Solve each equation. Check your solutions.
69.
ANSWER:
ANSWER:
60
70.
66. Which graph represents the solution set for
ANSWER:
A
71.
B
ANSWER:
C
D
Name the property illustrated by each
ANSWER:
A statement.
72. If then
HEALTHThe National Heart Association
67.
recommends that less than 30% of a person s total ANSWER:
’ Addition (=)
daily caloric intake come from fat. One gram of fat
yields nine Calories. Consider a healthy 21-year-old
whose average caloric intake is between 2500 and 73. If and then
3300 Calories.
a
. Write an inequality that represents the suggested
fat intake for the person. ANSWER:
b Transitive (=)
. What is the greatest suggested fat intake for the
person? If
74. then
ANSWER:
a. ANSWER:
Assoc. (+)
b.110g
TRAVEL Maggie is planning a 5-day trip to a family
68.
reunion. She wants to spend no more than $1000.
Her plane ticket is $375, and the hotel is $85 per
night.
a
. Let f represent the cost of food for one day. Write
an inequality to represent this situation.
b
. Solve the inequality and interpret the solution.
ANSWER:
a.
b. She can spend no more than $40 per day on food.
Solve each equation. Check your solutions.
69.
ANSWER:
70.
ANSWER:
71.
ANSWER:
Name the property illustrated by each
statement.
72. If then
ANSWER:
Addition (=)
73. If and then
ANSWER:
Transitive (=)
74. If then
ANSWER:
Assoc. (+)
Solve each inequality. Graph the solution set on
a number line.
1.
ANSWER:
2.
ANSWER:
3. or
ANSWER:
4. or
ANSWER:
5.
ANSWER:
6.
ANSWER:
7.
ANSWER:
Solve each inequality. Graph the solution set on
a number line.
1.
ANSWER:
8.
ANSWER:
2.
9.
ANSWER:
ANSWER:
3. or
ANSWER:
10.
ANSWER:
4. or
ANSWER:
11. MONEYKhalid is considering several types of paint
for his bedroom. He estimates that he will need
between 2 and 3 gallons. The table at the right shows
the price per gallon for each type of paint Khalid is
considering. Write a compound inequality and
5. determine how much he could be spending.
ANSWER:
6.
ANSWER:
ANSWER:
between $43.96 and $77.94
Solve each inequality. Graph the solution set on
a number line.
7.
12.
ANSWER:
ANSWER:
8.
13.
ANSWER:
ANSWER:
9.
14. or
ANSWER:
ANSWER:
10.
15. or
ANSWER:
ANSWER:
11. MONEYKhalid is considering several types of paint
for his bedroom. He estimates that he will need 16.
between 2 and 3 gallons. The table at the right shows
the price per gallon for each type of paint Khalid is ANSWER:
considering. Write a compound inequality and
determine how much he could be spending.
17.
ANSWER:
ANSWER:
between $43.96 and $77.94 18.
Solve each inequality. Graph the solution set on ANSWER:
a number line.
12.
ANSWER:
19.
ANSWER:
13.
ANSWER:
20.
ANSWER:
14. or
ANSWER:
21.
15. or ANSWER:
ANSWER:
ANATOMYForensic scientists use the equation h
22.
= 2.6f + 47.2 to estimate the height h of a woman
16. given the length in centimeters f of her femur bone.
ANSWER: a
. Suppose the equation has a margin of error of 3
±
centimeters. Write an inequality to represent the
height of a woman given the length of her femur
bone.
b
. If the length of a female skeleton’s femur is 50
centimeters, write and solve an absolute value
17. inequality that describes the woman s height in
’
ANSWER: centimeters.
ANSWER:
a.
b.
18.
Write an absolute value inequality for each
ANSWER: graph.
23.
ANSWER:
19.
ANSWER:
24.
ANSWER:
25.
20.
ANSWER:
ANSWER:
26.
ANSWER:
21.
ANSWER:
27.
ANSWER:
28.
ANATOMYForensic scientists use the equation h
22.
= 2.6f + 47.2 to estimate the height h of a woman
given the length in centimeters f of her femur bone. ANSWER:
a
. Suppose the equation has a margin of error of 3
±
centimeters. Write an inequality to represent the
height of a woman given the length of her femur
bone. 29.
b ANSWER:
. If the length of a female skeleton’s femur is 50
centimeters, write and solve an absolute value
inequality that describes the woman’s height in
centimeters.
30.
ANSWER:
a. ANSWER:
b.
DOGS The Labrador retriever is one of the most
Write an absolute value inequality for each 31.
graph. recognized and popular dogs kept as a pet. Using the
information given, write a compound inequality to
23. describe the range of healthy weights for a fully
grown female Labrador retriever.
ANSWER:
24.
ANSWER:
ANSWER:
GEOMETRY The Exterior Angle Inequality
32.
25. Theorem states that an exterior angle measure is
greater than the measure of either of its
ANSWER: corresponding remote interior angles. Write two
inequalities to express the relationships among the
measures of the angles of ABC.
26.
ANSWER:
27.
ANSWER:
ANSWER:
Solve each inequality. Graph the solution set on
a number line.
33.
28.
ANSWER:
ANSWER:
29.
ANSWER:
34.
ANSWER:
30.
ANSWER:
35.
DOGS The Labrador retriever is one of the most ANSWER:
31.
recognized and popular dogs kept as a pet. Using the
information given, write a compound inequality to
describe the range of healthy weights for a fully
grown female Labrador retriever.
36.
ANSWER:
ANSWER:
37.
GEOMETRY The Exterior Angle Inequality
32.
Theorem states that an exterior angle measure is ANSWER:
greater than the measure of either of its
corresponding remote interior angles. Write two
inequalities to express the relationships among the
measures of the angles of ABC.
38.
ANSWER:
ANSWER:
39.
Solve each inequality. Graph the solution set on
ANSWER:
a number line.
33.
ANSWER:
40.
34.
ANSWER:
ANSWER:
1-6 Solving Compound and Absolute Value Inequalities
Write an algebraic expression to represent
35.
each verbal expression.
ANSWER: numbers that are at least 4 units from 5
41. –
ANSWER:
36. numbers that are no more than
42. unit from 1
ANSWER:
ANSWER:
43. numbers that are at least 6 units but no more than 10
37. units from 2
ANSWER: ANSWER:
AUTO RACINGNASCAR rules stipulate that a
44.
car must conform to a set of 32 templates, each
38. shaped to fit a different contour of the car. When a
template is placed on a car, the gap between it and
ANSWER: the car cannot exceed the specified tolerance. Each
template is marked on its edge with a colored line
that indicates the tolerance for the template.
39.
ANSWER:
a. Suppose a certain template is 24.42 inches long.
Use the information in the table at the right to write
an absolute value inequality for templates with each
line color.
b. Find the acceptable lengths for that part of a car if
40. the template has each line color.
c. Graph the solution set for each line color on a
number line.
ANSWER:
d
. The tolerance of which line color includes the
tolerances of the other line colors?
Explain your reasoning.
ANSWER:
a
Write an algebraic expression to represent .
each verbal expression.
numbers that are at least 4 units from 5
41. –
eSolutions Manual - Powered by Cognero Page4
ANSWER: b.
numbers that are no more than c.
42. unit from 1
ANSWER:
43. numbers that are at least 6 units but no more than 10
units from 2
d. Red; the red line color has the smallest tolerance,
ANSWER: , so the other line colors would be
well within their tolerances.
AUTO RACINGNASCAR rules stipulate that a
44. Solve each inequality. Graph the solution set on
car must conform to a set of 32 templates, each
shaped to fit a different contour of the car. When a a number line.
template is placed on a car, the gap between it and 45.
the car cannot exceed the specified tolerance. Each
ANSWER:
template is marked on its edge with a colored line
that indicates the tolerance for the template.
46.
ANSWER:
a. Suppose a certain template is 24.42 inches long.
Use the information in the table at the right to write
an absolute value inequality for templates with each 47.
line color.
b. Find the acceptable lengths for that part of a car if ANSWER:
the template has each line color.
c. Graph the solution set for each line color on a
number line.
d
. The tolerance of which line color includes the
tolerances of the other line colors? 48.
Explain your reasoning.
ANSWER:
ANSWER:
a
.
b. 49.
ANSWER:
c.
50.
ANSWER:
d. Red; the red line color has the smallest tolerance,
, so the other line colors would be
HEALTHHypoglycemia (low blood sugar) and
well within their tolerances. 51.
hyperglycemia (high blood sugar) are potentially
Solve each inequality. Graph the solution set on dangerous and occur when a person’s blood sugar
fluctuates by more than 38 mg from the normal blood
a number line. sugar level of 88 mg. Write and solve an absolute
45. value inequality to describe blood sugar levels that
ANSWER: are considered potentially dangerous.
ANSWER:
AIR TRAVELThe airline on which Drew is flying
52.
46. has weight restrictions for checked baggage. Drew is
checking one bag.
ANSWER: a. Describe the range of weights that would classify
Drew s bag as free, $25, $50, and unacceptable.
’
b
. If Drew s bag weighs 68 pounds, how much will
’
he pay to take it on the plane?
47.
ANSWER:
48.
ANSWER:
ANSWER:
a.
b. $25
53. ERROR ANALYSISDavid and Sarah are solving
. Is either of them
49.
correct? Explain your reasoning.
ANSWER:
50. ANSWER:
Sample answer: David; when Sarah converted the
ANSWER: absolute value into two inequalities, she mistakenly
switched
the inequality symbols.
54. CHALLENGESolve
HEALTHHypoglycemia (low blood sugar) and
51.
hyperglycemia (high blood sugar) are potentially ANSWER:
dangerous and occur when a person’s blood sugar x < 0
fluctuates by more than 38 mg from the normal blood
sugar level of 88 mg. Write and solve an absolute REASONING Determine whether each
value inequality to describe blood sugar levels that statement is true or false. If false, provide a
are considered potentially dangerous. counterexample.
55. The graph of a compound inequality involving an and
ANSWER: statement is bounded on the left and right by two
values of x.
ANSWER:
AIR TRAVELThe airline on which Drew is flying
52. False; sample answer: the graph of
has weight restrictions for checked baggage. Drew is x > 2 and x > 5 is a ray bounded only on one end.
checking one bag.
a. Describe the range of weights that would classify
Drew s bag as free, $25, $50, and unacceptable. 56. The graph of a compound inequality involving an or
’ statement contains a region of values that are not
b
. If Drew s bag weighs 68 pounds, how much will
’ solutions.
he pay to take it on the plane?
ANSWER:
False; sample answer: the graph of
x > 2 or x < 3 includes the entire number line.
57. The graph of a compound inequality involving an and
statement includes values that make all parts of the
given statement true.
ANSWER:
True
ANSWER:
a. 58. WRITING IN MATHAn alternate definition of
b. $25 absolute value is to define as the distance
between a and b on the number line. Explain how
53. ERROR ANALYSISDavid and Sarah are solving this definition can be used to solve inequalities of the
. Is either of them form .
correct? Explain your reasoning.
ANSWER:
Sample answer: represents
the distance between some unknown value of the
variable x and a point c on the number line. The
solution set of the inequality is the set of all numbers
such that the distance from the numbers to c is less
ANSWER: than r units. Use a number line to find the numbers
Sample answer: David; when Sarah converted the that are r units from c in either direction.
absolute value into two inequalities, she mistakenly
switched 59. REASONINGThe graphs of the solutions of two
the inequality symbols. different absolute value inequalities are shown.
Compare and contrast the absolute value inequalities.
54. CHALLENGESolve
ANSWER:
x < 0
REASONING Determine whether each ANSWER:
Sample answer: The graph on the left indicates a
statement is true or false. If false, provide a solution set from –3 to 5. The
counterexample. graph on the right indicates a solution
55. The graph of a compound inequality involving an and set of all numbers less than or equal to
statement is bounded on the left and right by two –3 or greater than or equal to 5.
values of x.
ANSWER: OPEN ENDED
60. Write an absolute value inequality
False; sample answer: the graph of with a solution of
x > 2 and x > 5 is a ray bounded only on one end.
ANSWER:
56. The graph of a compound inequality involving an or Sample answer:
statement contains a region of values that are not
solutions.
ANSWER:
61. WHICH ONE DOESN’T BELONG?Identify the
False; sample answer: the graph of compound inequality that is not the same as the other
x > 2 or x < 3 includes the entire number line. three. Explain your reasoning.
57. The graph of a compound inequality involving an and
statement includes values that make all parts of the
given statement true.
ANSWER:
ANSWER:
True Each of these has a non-empty solution set except
for x > 5 and x < 1. There are no values of x that are
simultaneously greater than 5 and less than 1.
58. WRITING IN MATHAn alternate definition of
absolute value is to define as the distance
between a and b on the number line. Explain how 62. WRITING IN MATHSummarize the difference
this definition can be used to solve inequalities of the between and compound inequalities and or
form . compound inequalities.
ANSWER:
ANSWER: Sample answer: A compound inequality that contains
and is true if and only if both individual inequalities
Sample answer: represents are true, while an inequality containing or only needs
the distance between some unknown value of the one of the individual inequalities to be true.
variable x and a point c on the number line. The
solution set of the inequality is the set of all numbers 63. Which of the following best describes the graph of
such that the distance from the numbers to c is less the equations below?
than r units. Use a number line to find the numbers
that are r units from c in either direction.
59. REASONINGThe graphs of the solutions of two AThe lines have the same x-intercept.
different absolute value inequalities are shown. B The lines have the same y-intercept.
Compare and contrast the absolute value inequalities. C The lines are parallel.
D The lines are perpendicular.
ANSWER:
C
ANSWER: 64. SAT/ACT Find an expression equivalent
Sample answer: The graph on the left indicates a
solution set from –3 to 5. The to
graph on the right indicates a solution
set of all numbers less than or equal to
–3 or greater than or equal to 5.
F
OPEN ENDED
60. Write an absolute value inequality
with a solution of G
ANSWER: H
Sample answer:
J
61. WHICH ONE DOESN’T BELONG?Identify the K
compound inequality that is not the same as the other
three. Explain your reasoning.
ANSWER:
K
ANSWER:
65. GRIDDED RESPONSEHow many cubes that
Each of these has a non-empty solution set except measure 4 centimeters on each side can be placed
for x > 5 and x < 1. There are no values of x that are completely inside the box below?
simultaneously greater than 5 and less than 1.
62. WRITING IN MATHSummarize the difference
between and compound inequalities and or
compound inequalities.
ANSWER:
Sample answer: A compound inequality that contains ANSWER:
and is true if and only if both individual inequalities 60
are true, while an inequality containing or only needs 66. Which graph represents the solution set for
one of the individual inequalities to be true.
63. Which of the following best describes the graph of A
the equations below?
B
A
The lines have the same x-intercept. C
B The lines have the same y-intercept.
C The lines are parallel. D
D The lines are perpendicular. ANSWER:
A
ANSWER:
C
HEALTHThe National Heart Association
67.
SAT/ACT Find an expression equivalent recommends that less than 30% of a person’s total
64. daily caloric intake come from fat. One gram of fat
yields nine Calories. Consider a healthy 21-year-old
to whose average caloric intake is between 2500 and
3300 Calories.
a
. Write an inequality that represents the suggested
F
fat intake for the person.
b
. What is the greatest suggested fat intake for the
person?
G
ANSWER:
H a.
b.110g
J
TRAVELMaggie is planning a 5-day trip to a family
68.
reunion. She wants to spend no more than $1000.
K Her plane ticket is $375, and the hotel is $85 per
night.
a
. Let f represent the cost of food for one day. Write
an inequality to represent this situation.
b
. Solve the inequality and interpret the solution.
ANSWER:
K
ANSWER:
a.
GRIDDED RESPONSEHow many cubes that
65. b. She can spend no more than $40 per day on food.
measure 4 centimeters on each side can be placed
completely inside the box below? Solve each equation. Check your solutions.
69.
ANSWER:
ANSWER:
60 70.
Which graph represents the solution set for ANSWER:
66.
A
71.
B
ANSWER:
C
D Name the property illustrated by each
ANSWER:
statement.
A If then
72.
ANSWER:
HEALTHThe National Heart Association
67.
recommends that less than 30% of a person s total Addition (=)
’
daily caloric intake come from fat. One gram of fat
yields nine Calories. Consider a healthy 21-year-old
whose average caloric intake is between 2500 and 73. If and then
3300 Calories.
a
. Write an inequality that represents the suggested
fat intake for the person. ANSWER:
b Transitive (=)
. What is the greatest suggested fat intake for the
person? If
74. then
ANSWER:
a. ANSWER:
Assoc. (+)
b.110g
TRAVEL Maggie is planning a 5-day trip to a family
68.
reunion. She wants to spend no more than $1000.
Her plane ticket is $375, and the hotel is $85 per
night.
a
. Let f represent the cost of food for one day. Write
an inequality to represent this situation.
b
. Solve the inequality and interpret the solution.
ANSWER:
a.
b. She can spend no more than $40 per day on food.
Solve each equation. Check your solutions.
69.
ANSWER:
70.
ANSWER:
71.
ANSWER:
Name the property illustrated by each
statement.
72. If then
ANSWER:
Addition (=)
73. If and then
ANSWER:
Transitive (=)
74. If then
ANSWER:
Assoc. (+)
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