Intermediate algebra 7th edition by martin gay solution manual

The addition property of equality allows us to add the same number to or subtract the same number from both sides of an equation and have an equivalent equation.. The multiplication prop

variable x might have Thus, there is no solution

The solution set is { } or ∅

x, all real numbers are solutions The solution set

is the set of all real numbers or

{x|x is a real number}

Vocabulary, Readiness & Video Check 2.1

1. Equations with the same solution set are called

equivalent equations

2. A value for the variable in an equation that

makes the equation a true statement is called a

solution of the equation

3. By the addition property of equality, y = −3 and

y − 7 = −3 − 7 are equivalent equations

4. By the multiplication property of equality,

9. The addition property of equality allows us to

add the same number to (or subtract the same

number from) both sides of an equation and have

an equivalent equation The multiplication

property of equality allows us to multiply (or

divide) both sides of an equation by the same

nonzero number and have an equivalent

equation

10 distributive property

11 to make the calculations less tedious

12 When solving a linear equation and all variable

terms subtract out and:

a. you have a true statement, then the equation

has all real numbers for which the equation

8.6 8.6 6.3 8.6

2.3

y y

y

− = −

=Check: 8.6 6.32.3 8.6 6.36.3 6.3 True

y − = −

− = −ⱨThe solution is 2.3

x

ⱨⱨThe solution is 2.1

x x

x x

4 4

+ =

⋅ + ⋅+

5 102(4 ) 70

7 7010

r r

r r

r r

r r r r

Check: 4 7

5 104(10) 10

x x

0.3(8) 2.4 0.1(8) 4

2.4 2.4 0.8 44.8 4.8 True

Check: 2.4(2 3) 0.1(2 3)2.4(2( 1.5) 3) 0.1(2( 1.5) 3)2.4( 3 3) 0.1( 3 3)2.4(0) 0.1(0)

y y

70 The difference means to subtract The difference of 8 and a number: 8 − x

72 Two more than three times a number: 3x + 2

Subtracting 2 from a number and subtracting 7 from the same number will not result in equal numbers for any

value of x There is no solution

82 answers may vary

84 answers may vary

From this we see that K = 24

90 answers may vary

x x

= − +

=

=Check: 1.25 20.175 8.15

plus third integer odd

2. If x = number of passengers at Los Angeles International Airport, in millions, then

x + 3.1 = passengers at Chicago’s O’Hare airport, and

2x − 31.9 = passengers at Atlanta’s Hartsfield-Jackson airport

Then x + (x + 3.1) + (2x − 31.9) = x + x + 3.1 + 2x − 31.9 = 4x − 28.8

3. Let x = the first number, then 3x − 8 = the second number, and 5x = the third number

The sum of the three numbers is 118

(3 8) 5 118

9 8 118

9 12614

x x x

The numbers are 14, 3x − 8 = 3(14) − 8 = 34, and 5x = 5(14) = 70

4. Let x = the original price Then 0.4x = the discount The original price, minus the discount, is equal to $270

0.4 270

0.6 270

2704500.6

The original price was $450

5. Let x = width, then 2x − 16 = length

The perimeter is 160 inches

2( ) 2(2 16) 160

2 4 32 160

6 32 160

6 19232

x x x

The width is 32 inches and the length is 48 inches

6. Let x = first odd integer, then x + 2 = second odd integer, and x + 4 = third odd integer

The sum of the integers is 81

( 2) ( 4) 81

3 6 81

3 7525

x x x

The integers are 25, 27, and 29

Vocabulary, Readiness & Video Check 2.2

1. 130% of a number > the number

2. 70% of a number < the number

3. 100% of a number = the number

4. 200% of a number > the number

First Integer All Described

14 The original application asks you to find three numbers The solution x = 45 only gives you the first number You

need to INTERPRET this result

4. Let x = first odd integer, then

x + 2 = second odd integer, and

x + 4 = third odd integer

12 Let x = the number

14 Let x = the first number, then

x − 6 = the second number, and

2x = the third number

( 6) 2 306

4 6 306

4 31278

x x x

Approximately 284 tornadoes occurred in the

United States during June 2014

20 Let x be the number of people employed in the

restaurant industry Then x is 10% of

147 million

x = 0.10(147 million) = 14.7 million

There were 14.7 million people employed in the

restaurant industry in the U.S in 2014

22 From the circle graph, 39% of time is spent on

x x x

x x x

x x x

The sides measure 16 centimeters,

28 centimeters, and 31 centimeters

30 7.3 (9.2 3) 7.3 (9.2 3) 324

33 6 324

33 33010

x x x

The sides measure 73 feet, 73 feet, 89 feet, and

89 feet

32 Let x = the first odd integer, then

x + 2 = the second odd integer and

x + 4 = the third odd integer

3 6 327

3 321107

x x x

+ + + + =

+ =

=

=The numbers are 107, 109, 111

34 Let x = first integer, then

x + 1 = second integer, and

x x x

3 11 2 11 66

6 6611

x x

Year

Percent of Increase

in Social Network Users

Predicted Percent of Increase

Total 66%

38 Let x be the decline in the number of travel agent

jobs (in hundreds) Then x − 17 is the decline in

the number of reporter or correspondent jobs and

2x − 21 is the decline in the number of flight

x x x

The predicted declines are:

travel agent jobs: 89 hundred;

reporter or correspondent jobs: 72 hundred

flight attendant jobs: 157 hundred

40 Let x be the number of seats in Gillette Stadium

Then x + 11,200 is the number of seats in AT&T

Stadium and x − 3800 is the number of seats at

x x x

Gillette Stadium seats 68,800, AT&T Stadium

seats 80,000, and CenturyLink Field seats

tax

44 Let x be the population in 2004

This population, decreased by 1.96%, is the 2014 population of 80.9 million

=

≈The population of Germany in 2004 was 82.5 million

46 Let x be the size of the workforce prior to

layoffs

0.15 11,00073,333

x x

=

≈Prior to layoffs, Dana’s workforce was 73,333 people

48 Let x = measure of complement; then

2x + 30 = measure of angle

3 6020

x x

=

=

2x + 30 = 2(20) + 30 = 70

The angles measure 20° and 70°

50 Let x = base angle; then 3x − 10 = third angle

2 3 10 180

5 10 180

5 19038

x x x

The angles measure 38°, 38°, and 104°

52 Let x = length of side of pentagon, then

x + 7 = length of side of square

54 Let x = first integer, then

x + 1 = second integer, and

x + 2 = third integer, and

x + 3 = fourth integer

( 1) ( 3) 110

2 4 110

2 10653

x x x

56 Let x be the payroll for the Montreal Canadiens

Then x − 5,049,585 was the payroll for the San

x x

x

x x

Canadiens was $67,132,652 and the payroll for

the San Jose Sharks was $62,083,067

58 Let x be the number of passengers at Los

Angeles International Airport, in millions

Then x + 3.1 is the number of passengers at

Chicago’s O’Hare airport, and 2x − 31.9 is the

number of passengers at Atlanta’s

x x x

The numbers of passengers are:

Los Angeles: 63.7 million;

x x x

The bases measure 18.5 meters and 37 meters,

and the sides measure 20.5 meters and

34 meters

62 Let x be the energy cost of an LED bulb Then

x + 26 is the energy cost of a CFL bulb, and

6x + 18 is the energy cost of an incandescent

bulb

8 44 476

8 43254

x x x

64 Let x be the number of medals won by the

Netherlands Then Canada won x + 1 medals and Norway won x + 2 medals

3 3 75

3 7224

x x x

66 Let x = height, then 2x + 12 = length

2( ) 2(2 12) 312

6 24 312

6 28848

x x x

74 answers may vary

76 Let x° be the measure of an angle Then its

complement measures (90 − x)° and its supplement measures (180 − x)°

78 y = −80.6x + 2054

y = −80.6(17) + 2054 ≈ 684 The average number of cigarettes smoked by an American adult is predicted to be 684 in 2017

80 The average number of cigarettes smoked daily

in 2017 is predicted to be 684 2

365≈This does not represent the average number of

cigarettes smoked by an American smoker,

because it is the average for all Americans, both

smokers and non-smokers

82 Let x be the first odd integer Then x + 2 is the

next consecutive odd integer

500 computer boards must be sold to break even

It costs $30,000 to produce the 500 boards

86 The company makes a profit if it makes and sells

more products than the break-even number

Section 2.3 Practice Exercises

8000 1

28000(1.03)8000(1.266770081)10,134.16

nt r

n A

A A A

Russ will have $10,134.16 in his account

5. Let d = 190 and r = 7.5

190 7.5

190 7.57.5 7.51253

6. 4 0

44

7. That the specified variable will equal some

expression and that this expression should not

contain the specified variable

8. The only way to check the solution is in the

formula used, because if the wrong formula is

used, a wrong answer may seem to check

( 1)( 1)

55

b H

2 2

22

− π

=π

A P t Pr

The amount in the account is $27,623.53

30 Roundtrip distance = 154 + 154 = 308 miles

Their average speed was 56 mph

32 Using the formula 9 32,

The temperature was 5°F

34 The total area of the ceiling is

18(12) = 216 square feet Each package can

cover up to 50 square feet Thus, the number of

packages needed is 216 4.32

50 = Therefore,

5 packages must be purchased

36 Using the formula 1 ,

nt r

Yes, the amount is enough

38 Note that the wall covers 21 ⋅ 8 = 168 square

feet Because we wish to paint three coats, we

actually must cover a total of

168 ⋅ 3 = 504 square feet Since each gallon covers 300 square feet, we need

5041.68 gallons

300= of paint 2 gallons should be purchased

( )

h h h h

( )( )

V V V

V V

= π

= π

≈The volume of the cylinder is 753.98 cubic millimeters

3

43443

268 08

( )

V V

= π

= π

≈The volume of the sphere is 268.08 cubic millimeters

The drill can be removed at a rate of 1.6 ft/sec

50 Using the formula 4 3,

64 answers may vary

Planet AU from Sun

74 answers may vary

76 answers may vary

78 Two of the 8 sectors are yellow

2 1yellow)

8 4(

80 Three of the 8 sectors are blue

3blue)8(

82 Three of the sectors are black or yellow

3black or yellow)

8(

84 Six of the sectors are yellow, blue, or black

6 3yellow, blue, or black)

8 4(

86 All of the sectors are red, yellow, green, blue, or

black

8red, yellow, green, blue, or black) 1

8(

88 P(event sure to occur) = 1

Section 2.4 Practice Exercises

1 a. {x|x < 3.5} (−∞, 3.5)

3.5)

b {x|x ≥ −3} [−3, ∞)

–3

c {x|−1 ≤ x < 4} [−1, 4)

4)–1

x x x

≥

⋅ ≥ ⋅

≥2

–4(

≥Sales must be greater than or equal to $10,000 per month

− + <

− < −

>

The annual consumption of cigarettes will be less than 175 billion more than 18.2 years after 2004, or in

approximately 18 + 2004 = 2022 and after

Vocabulary, Readiness & Video Check 2.4

9. The graph of Example 1 is shaded from −∞ to,

but not including, −3, as indicated by a

parenthesis To write interval notation, write

down what is shaded for the inequality from left

to right A parenthesis is always used with −∞,

so from the graph, the interval notation is

(−∞, −3)

10 We can add the same number to (or subtract the

same number from) both sides of a linear

inequality in one variable and have an equivalent

inequality; addition property of equality

11 If you multiply or divide both sides of an

inequality by the same nonzero negative number,

you must reverse the direction of the inequality

10 {x|−3 > x ≥ −7}

[−7, −3)

–3

)–7

12 2 1

3

x x

+ ≤ −

≤ −(−∞, −3]

≥

⋅ ≥ ⋅

≥[6, ∞)

6

20 4 11.2

2.8

x x

> −

> −(−2.8, ∞)

–2.8(

–2

24 8 5 23

5 153

x x x

− ≤

≥ −[−3, ∞)

30 5( 4) 4(2 3)

83

x x

x x x

⎛−∞ ⎤

1,2

x x x

14,3

5 ( 1) 5( 1)5

4( 1) 5( 1)

4 511

48 0.7 0.45

0.3 0.45

1.5

x x x x

− >

− >

< −(−∞, −1.5)

+ ≤ − ++ ≤ −

≤ −

≤ −(−∞, −17]

,6

,3

∞⎟

⎢⎣ ⎠

70 a Let x be Holden’s time on his last trial

6.85 7.04 6.92

74

6.85 7.04 6.92

46.85 7.04 6.92 28

20.81 20.81 28 20.81

7.19

x x x x x

b A time of 7.19 minutes or less will result in

an average time under 7.0 minutes

72 a Let x be the number of additional ouces

98 21 300

21 202

approximately 9.6

x x x

≤

≤

The solution is {x|x ≤ 9.6}

b Since x represents the number of ounces

after the first ounce, you can mail at most

1 ounce plus 9 additional ounces, or

x

x x x

b Since x represents the number of half hours

after the first hour, you can park for at most

1 hour plus 5 additional half hours, or

{n|n > 200}

b. Plan 1 is more economical than Plan 2 when

200 or more calls are made

78 Given that F ≥ 977, we know the following:

5( 32)9

5(977 32)9

5(945)9525

C C C

t t t

− + <

− < −

>

2004 + 28.8 = 2032.8 The consumption will be less than 50 billion during the year 2032 and after

b answers may vary

82 Consumption of skim milk is decreasing over time; answers may vary

84 2024 is 20 years after 2004, so 2024 corresponds

to t = 20

s = −0.22t + 27.4

s = −0.22(20) + 27.4 = −4.4 + 27.4 = 23 The average consumption of skim milk is predicted to be 23 pounds per person per year in

2024

86 answers may vary

88 answers may vary

90 answers may vary

x x x

106 To solve 3x > −14, both sides must be divided by

3, so the inequality symbol will not be reversed

108 To solve −x ≤ 9, both sides must be divided by

−1, so the inequality symbol will be reversed

The solution set is (4, ∞)

112 answers may vary

114 answers may vary

116 answers may vary

4

83

x x

x x

x x

+ ≥ ++ ≥

≥ −[−1, ∞)

20 2

110

x x x

− ≤

≥ −1,10

2

16

x x x x

1,6

x

x

x x

x x x x

x x x

−+ <

,32

{x|x < 2}, (−∞, 2)

2)

{x|x < 5 and x < 2} = {x|x < 2}

2

)The solution set is (−∞, 2)

The numbers that are in either set or both sets are

{1, 2, 3, 4, 5, 6, 7, 9} This set is the union,

{x|x < 2 or x > 0}, (−∞, ∞)

The solution set is (−∞, ∞)

Vocabulary, Readiness & Video Check 2.5

1. Two inequalities joined by the words “and” or

“or” are called compound inequalities

2. The word and means intersection

3. The word or means union

4. The symbol ∩ means intersection

5. The symbol ∪ represents union

6. The symbol ∅ is the empty set

7. For an element to be in the intersection of sets A and B, the element must be in set A and in set B

8. Graph the two intervals, each on its own number line, so you can see their intersection Graph this intersection on the third number line⎯this intersection is the solution set

9. For an element to be in the union of sets A and

B , the element must be in set A or in set B

10 Graph the two intervals, each on its own number

line, so you can see their union Graph this union

on the third number line⎯this union is the solution set

x x

x x x x

38 x ≥ −3 or x ≤ −4

(−∞, −4] ∪ [−3, ∞)

–3 –4

x <

5,7

⎛−∞ ⎞

x x x x

x x x x

x x

x x x

⎡− ⎞

⎟

x x x

82 From the graph, we see that the number of

single-family housing starts were less than 500

or the number of single-family housing

completions greater than 1500 are for the years

252

480 2 327 534

153 2 20776.5 103.576.5 100

x x x x x

If Wendy scores between 76.5 and 100 inclusive

on her final exam, she will receive a B in the course

Section 2.6 Practice Exercises

6. 3 9 7

23

The absolute value of a number is never

negative, so there is no solution The solution set

is { } or ∅

84

x +

= −

The absolute value of a number is never

negative, so there is no solution The solution set

x x x

+ = − −+ = − ++ =

Vocabulary, Readiness & Video Check 2.6

− + =

− = −which is impossible

The solution set is ∅

18 3 2 0

23

y y y y

+ =+ =

= −

= −