Elementary and Intermediate Algebra

Marvin L. Bittinger, David J. Ellenbogen,Barbara L. Johnson

Chapter 1 Introduction to Algebraic Expressions - all with Video Answers

Educators

Section 1

Introduction to Algebra

00:38

Problem 1

Classify each of the following as either an expression or an equation.
$$
4 x+7
$$

Destini Smith

Numerade Educator

00:43

Problem 2

Classify each of the following as either an expression or an equation.
$$
3 x=21
$$

Veronica Santana

Numerade Educator

01:52

Problem 3

Classify each of the following as either an expression or an equation.
$$
2 x-5=9
$$

Quinn Langford

Numerade Educator

01:00

Problem 4

Classify each of the following as either an expression or an equation.
$$
5(x-2)
$$

Veronica Santana

Numerade Educator

01:36

Problem 5

Classify each of the following as either an expression or an equation.
$$
38=2 t
$$

Quinn Langford

Numerade Educator

00:48

Problem 6

Classify each of the following as either an expression or an equation.
$$
45=a-1
$$

Veronica Santana

Numerade Educator

02:07

Problem 7

Classify each of the following as either an expression or an equation.
$$
4 a-5 b
$$

Quinn Langford

Numerade Educator

00:43

Problem 8

Classify each of the following as either an expression or an equation.
$$
3 t+4=19
$$

Julie Silva

Numerade Educator

02:13

Problem 9

Classify each of the following as either an expression or an equation.
$$
2 x-3 y=8
$$

Quinn Langford

Numerade Educator

00:48

Problem 10

Classify each of the following as either an expression or an equation.
$$
12-4 x y
$$

Veronica Santana

Numerade Educator

02:41

Problem 11

Classify each of the following as either an expression or an equation.
$$
r(t+7)+5
$$

Quinn Langford

Numerade Educator

00:40

Problem 12

Classify each of the following as either an expression or an equation.
$$
9 a+b
$$

Veronica Santana

Numerade Educator

01:03

The Try Exercises for examples are indicated by a shaded block on the exercise number. Answers to these exercises appear at the end of the exercise set as well as at the back of the book.
$3 a,$ for $a=9$

Quinn Langford

Numerade Educator

00:42

Problem 14

Veronica Santana

Numerade Educator

01:03

Problem 15

Quinn Langford

Numerade Educator

00:40

Problem 16

Veronica Santana

Numerade Educator

00:43

Problem 17

Quinn Langford

Numerade Educator

00:53

Problem 18

Veronica Santana

Numerade Educator

00:44

Problem 19

Quinn Langford

Numerade Educator

00:58

Problem 20

Veronica Santana

Numerade Educator

00:51

Problem 21

Quinn Langford

Numerade Educator

00:55

Problem 22

Veronica Santana

Numerade Educator

02:10

Problem 23

Evaluate using a calculator.
$$
27 a-18 b, \text { for } a=136 \text { and } b=13
$$

Quinn Langford

Numerade Educator

01:37

Problem 24

Evaluate using a calculator.
$$
19 x y-9 x+13 y, \text { for } x=87 \text { and } y=29
$$

Veronica Santana

Numerade Educator

01:20

Problem 25

Substitute to find the value of each expression.
Basketball. The area of a rectangle with base $b$ and height $h$ is $b h .$ A regulation basketball backboard is 6 ft wide and $3 \frac{1}{2}$ ft high. Find the area of the backboard. Source: NBA

Quinn Langford

Numerade Educator

01:33

Problem 26

Substitute to find the value of each expression.
Travel Time. The length of a flight from Seattle, Washington, to St. Paul, Minnesota, is approximately $1400 \mathrm{mi} .$ The time, in hours, for the flight is
$$
\frac{1400}{v}
$$
where $v$ is the velocity, in miles per hour. How long will a flight take at a velocity of $400 \mathrm{mph} ?$

Veronica Santana

Numerade Educator

01:27

Problem 27

Substitute to find the value of each expression.
Zoology. A great white shark has triangular teeth. Each tooth measures about $5 \mathrm{cm}$ across the base and has a height of $6 \mathrm{cm} .$ Find the surface area of the front side of one such tooth. (See Example $3 .)$

Quinn Langford

Numerade Educator

01:52

Problem 28

Substitute to find the value of each expression.
Work Time. Alan takes twice as long to do a job as Connor does. Suppose $t$ represents the time it takes Connor to do the job. Then $2 t$ represents the time it takes Alan. How long does it take Alan if Connor takes (a) $30 \sec ?$ (b) $35 \min ?$ (c) $2 \frac{1}{2}$ hr?

Veronica Santana

Numerade Educator

01:51

Problem 29

Substitute to find the value of each expression.
Area of a Parallelogram. The area of a parallelogram with base $b$ and height $h$ is $b h .$ Edward Tufte's sculpture Spring Arcs is in the shape of a parallelogram with base $67 \mathrm{ft}$ and height 12 ft. What is the area of the parallelogram?

Quinn Langford

Numerade Educator

01:41

Problem 30

Substitute to find the value of each expression.
Olympic Softball. A softball player's batting average is $h / a,$ where $h$ is the number of hits and $a$ is the number of "at bats." In the 2008 Summer Olympics, Jessica Mendoza had 8 hits in 22 at bats. What was her batting average? Round to the nearest thousandth.

Veronica Santana

Numerade Educator

00:59

Problem 31

Translate to an algebraic expression.
5 more than Ron's age

Quinn Langford

Numerade Educator

00:47

Problem 32

Translate to an algebraic expression.
8 times Luke's speed

Veronica Santana

Numerade Educator

00:39

Problem 33

Translate to an algebraic expression.
The product of 4 and $a$

Quinn Langford

Numerade Educator

00:43

Problem 34

Translate to an algebraic expression.
7 more than Lou's weight

Veronica Santana

Numerade Educator

00:39

Problem 35

Translate to an algebraic expression.
9 less than $c$

Quinn Langford

Numerade Educator

00:54

Problem 36

Translate to an algebraic expression.
4 less than $d$

Jennifer Stoner

Numerade Educator

00:30

Problem 37

Translate to an algebraic expression.
6 increased by $q$

Quinn Langford

Numerade Educator

00:46

Problem 38

Translate to an algebraic expression.
11 increased by $z$

Veronica Santana

Numerade Educator

00:39

Problem 39

Translate to an algebraic expression.
The difference of $m$ and $n$

Quinn Langford

Numerade Educator

00:45

Problem 40

Translate to an algebraic expression.
$t$ subtracted from $p$

Veronica Santana

Numerade Educator

00:49

Problem 41

Translate to an algebraic expression.
$x$ less than $y$

Quinn Langford

Numerade Educator

00:41

Problem 42

Translate to an algebraic expression.
2 less than Lorrie's age

Veronica Santana

Numerade Educator

00:59

Problem 43

Translate to an algebraic expression.
$x$ divided by $w$

Quinn Langford

Numerade Educator

00:36

Problem 44

Translate to an algebraic expression.
The quotient of two numbers

Veronica Santana

Numerade Educator

00:43

Problem 45

Translate to an algebraic expression.
The sum of the box's length and height

Quinn Langford

Numerade Educator

00:21

Problem 46

Translate to an algebraic expression.
The sum of $d$ and $f$

Veronica Santana

Numerade Educator

01:44

Problem 47

Translate to an algebraic expression.
Panya's speed minus twice the wind speed

Quinn Langford

Numerade Educator

00:46

Problem 48

Translate to an algebraic expression.
The product of 9 and twice $m$

Veronica Santana

Numerade Educator

Problem 49

Translate to an algebraic expression.
Twelve less than a quarter of some number

Check back soon!

01:13

Problem 50

Translate to an algebraic expression.
Twenty less than six times a number

Veronica Santana

Numerade Educator

01:21

Problem 51

Translate to an algebraic expression.
Eight times the difference of two numbers

Quinn Langford

Numerade Educator

00:52

Problem 52

Translate to an algebraic expression.
One third of the sum of two numbers

Veronica Santana

Numerade Educator

01:13

Problem 53

Translate to an algebraic expression.
$64 \%$ of the women attending

Breanna Ollech

Numerade Educator

00:50

Problem 54

Translate to an algebraic expression.
$38 \%$ of a number

Veronica Santana

Numerade Educator

01:24

Problem 55

Determine whether the given number is a solution of the given equation.
$$
15 ; x+17=32
$$

Quinn Langford

Numerade Educator

00:55

Problem 56

Determine whether the given number is a solution of the given equation.
$$
75 ; y+28=93
$$

Veronica Santana

Numerade Educator

01:42

Problem 57

Determine whether the given number is a solution of the given equation.
$$
93 ; a-28=75
$$

Quinn Langford

Numerade Educator

00:48

Problem 58

Determine whether the given number is a solution of the given equation.
$$
12 ; 8 t=96
$$

Veronica Santana

Numerade Educator

01:06

Problem 59

Determine whether the given number is a solution of the given equation.
$$
63 ; \frac{t}{7}=9
$$

Quinn Langford

Numerade Educator

00:43

Problem 60

Determine whether the given number is a solution of the given equation.
$$
52 ; \frac{x}{8}=6
$$

Veronica Santana

Numerade Educator

02:10

Problem 61

Determine whether the given number is a solution of the given equation.
$$
3 ; \frac{108}{x}=36
$$

Quinn Langford

Numerade Educator

01:22

Problem 62

Determine whether the given number is a solution of the given equation.
$$
7 ; \frac{94}{y}=12
$$

Veronica Santana

Numerade Educator

01:06

Problem 63

Translate each problem to an equation. Do not solve.
Seven times what number is $1596 ?$

Quinn Langford

Numerade Educator

01:08

Problem 64

Translate each problem to an equation. Do not solve.
What number added to 73 is $201 ?$

Veronica Santana

Numerade Educator

01:01

Problem 65

Translate each problem to an equation. Do not solve.
When 42 is multiplied by a number, the result is 2352 . Find the number.

Quinn Langford

Numerade Educator

00:57

Problem 66

Translate each problem to an equation. Do not solve.
When 42 is multiplied by a number, the result is 2352 . Find the number.

Veronica Santana

Numerade Educator

01:11

Problem 67

Translate each problem to an equation. Do not solve.
Chess. A chess board has 64 squares. If pieces occupy 19 squares, how many squares are unoccupied?

Quinn Langford

Numerade Educator

01:00

Problem 68

Translate each problem to an equation. Do not solve.
Hours Worked. A carpenter charges $\$ 35$ an hour. How many hours did she work if she billed a total of $\$ 3150 ?$

Veronica Santana

Numerade Educator

04:27

Problem 69

Translate each problem to an equation. Do not solve.
Recycling. Currently, Americans recover $33.4 \%$ of all municipal solid waste. This is the same as recovering 85 million tons. What is the total amount of waste generated?

Quinn Langford

Numerade Educator

01:31

Problem 70

Translate each problem to an equation. Do not solve.
Travel to Work. For U.S. cities with populations greater than $5000,$ the longest average commute is 59.8 min in Indian Wells, Arizona. This is $51.2 \mathrm{min}$ longer than the shortest average commute, which is in Fort Bliss, Texas. How long is the average commute in Fort Bliss?

Veronica Santana

Numerade Educator

00:56

Problem 71

In each of Exercises $71-78,$ match the phrase or sentence with the appropriate expression or equation from the column on the right.
Twice the sum of
two numbers_____
a) $\frac{x}{y}+6$
b) $2(x+y)=48$
c) $\frac{1}{2} \cdot a \cdot b$
d) $t+2=5$
e) $a b-1=49$
f) $2(m+n)$
g) $3(t+5)$
h) $x-5=9$

Quinn Langford

Numerade Educator

00:41

Problem 72

In each of Exercises $71-78,$ match the phrase or sentence with the appropriate expression or equation from the column on the right.
Five less than a
number is nine._____
a) $\frac{x}{y}+6$
b) $2(x+y)=48$
c) $\frac{1}{2} \cdot a \cdot b$
d) $t+2=5$
e) $a b-1=49$
f) $2(m+n)$
g) $3(t+5)$
h) $x-5=9$

Veronica Santana

Numerade Educator

01:17

Problem 73

In each of Exercises $71-78,$ match the phrase or sentence with the appropriate expression or equation from the column on the right.
Two more than a
number is five._____
a) $\frac{x}{y}+6$
b) $2(x+y)=48$
c) $\frac{1}{2} \cdot a \cdot b$
d) $t+2=5$
e) $a b-1=49$
f) $2(m+n)$
g) $3(t+5)$
h) $x-5=9$

Quinn Langford

Numerade Educator

00:35

Problem 74

In each of Exercises $71-78,$ match the phrase or sentence with the appropriate expression or equation from the column on the right.
Half the product of two numbers_____
a) $\frac{x}{y}+6$
b) $2(x+y)=48$
c) $\frac{1}{2} \cdot a \cdot b$
d) $t+2=5$
e) $a b-1=49$
f) $2(m+n)$
g) $3(t+5)$
h) $x-5=9$

Veronica Santana

Numerade Educator

01:18

Problem 75

In each of Exercises $71-78,$ match the phrase or sentence with the appropriate expression or equation from the column on the right.
Three times the sum of a number and five_____
a) $\frac{x}{y}+6$
b) $2(x+y)=48$
c) $\frac{1}{2} \cdot a \cdot b$
d) $t+2=5$
e) $a b-1=49$
f) $2(m+n)$
g) $3(t+5)$
h) $x-5=9$

Quinn Langford

Numerade Educator

00:39

Problem 76

In each of Exercises $71-78,$ match the phrase or sentence with the appropriate expression or equation from the column on the right.
Twice the sum of two
numbers is 48_____
a) $\frac{x}{y}+6$
b) $2(x+y)=48$
c) $\frac{1}{2} \cdot a \cdot b$
d) $t+2=5$
e) $a b-1=49$
f) $2(m+n)$
g) $3(t+5)$
h) $x-5=9$

Veronica Santana

Numerade Educator

01:34

Problem 77

In each of Exercises $71-78,$ match the phrase or sentence with the appropriate expression or equation from the column on the right.
One less than the product of two numbers is 49_____
a) $\frac{x}{y}+6$
b) $2(x+y)=48$
c) $\frac{1}{2} \cdot a \cdot b$
d) $t+2=5$
e) $a b-1=49$
f) $2(m+n)$
g) $3(t+5)$
h) $x-5=9$

Quinn Langford

Numerade Educator

00:39

Problem 78

In each of Exercises $71-78,$ match the phrase or sentence with the appropriate expression or equation from the column on the right.
Six more than the quotient of two numbers_____
a) $\frac{x}{y}+6$
b) $2(x+y)=48$
c) $\frac{1}{2} \cdot a \cdot b$
d) $t+2=5$
e) $a b-1=49$
f) $2(m+n)$
g) $3(t+5)$
h) $x-5=9$

Veronica Santana

Numerade Educator

01:04

Problem 79

Nutrition. The number of grams $f$ of dietary fiber recommended daily for children depends on the age a of the child, as shown in the table below. Find an equation for $f$ in terms of $a$
CAN'T COPY THE TABLE

Lynn Larson

Numerade Educator

01:29

Problem 80

Tuition. The table below lists the tuition costs for students taking various numbers of hours of classes. Find an equation for the cost $c$ of tuition for a student taking $h$ hours of classes.
CAN'T COPY THE TABLE

Veronica Santana

Numerade Educator

04:28

Problem 81

Postage Rates. The U.S. Postal Service charges extra for packages that must be processed by hand. The table below lists machinable and nonmachinable costs for certain packages. Find an equation for the nonmachinable cost $n$ in terms of the machinable cost $m$
CAN'T COPY THE TABLE

Quinn Langford

Numerade Educator

01:29

Problem 82

Foreign Currency. On Emily's trip to France, she used her debit card to withdraw money. The table below lists the amounts $r$ that she received and the amounts $s$ that were subtracted from her account. Find an equation for $r$ in terms of $s$
CAN'T COPY THE TABLE

Veronica Santana

Numerade Educator

05:33

Problem 83

Number of Drivers. The table below lists the number of vehicle miles $v$ traveled annually per household by the number of drivers $d$ in the household. Find an equation for $v$ in terms of $d .$
CAN'T COPY THE TABLE

Quinn Langford

Numerade Educator

01:14

Problem 84

Meteorology. The table below lists the number of centimeters of water $w$ to which various amounts of snow $s$ will melt under certain conditions. Find an equation for $w$ in terms of $s$
CAN'T COPY THE TABLE

Veronica Santana

Numerade Educator

03:41

Problem 85

What is the difference between a variable, a variable expression, and an equation?

Quinn Langford

Numerade Educator

00:54

Problem 86

What does it mean to evaluate an algebraic expression?

Veronica Santana

Numerade Educator

03:42

Problem 87

If the lengths of the sides of a square are doubled, is the area doubled? Why or why not?

Quinn Langford

Numerade Educator

00:55

Problem 88

Write a problem that translates to $1998+t=2006$

Veronica Santana

Numerade Educator

05:33

Problem 89

Signs of Distinction charges $\$ 120$ per square foot for handpainted signs. The town of Belmar commissioned a triangular sign with a base of $3.0 \mathrm{ft}$ and a height of 2.5 ft. How much will the sign cost?
CAN'T COPY THE IMAGE

Quinn Langford

Numerade Educator

01:35

Problem 90

Find the area that is shaded in the figure below.
CAN'T COPY THE IMAGE

Veronica Santana

Numerade Educator

01:14

Problem 91

Evaluate $\frac{x+y}{2}$ when $y$ is twice $x$ and $x=6$

Quinn Langford

Numerade Educator

01:10

Problem 92

Evaluate $\frac{a-b}{3}$ when $a$ is three times $b$ and $a=18$

Veronica Santana

Numerade Educator

01:18

Problem 93

Answer each question with an algebraic expression.
If $w+3$ is a whole number, what is the next whole number after it?

Quinn Langford

Numerade Educator

00:52

Problem 94

Answer each question with an algebraic expression.
If $d+2$ is an odd number, what is the preceding odd number?

Veronica Santana

Numerade Educator

01:57

Problem 95

Translate to an algebraic expression.
The perimeter of a rectangle with length $l$ and width $w$ (perimeter means distance around)
CAN'T COPY THE IMAGE

Quinn Langford

Numerade Educator

00:33

Problem 96

Translate to an algebraic expression.
The perimeter of a square with side $s$ (perimeter means distance around)
CAN'T COPY THE IMAGE

Veronica Santana

Numerade Educator

01:20

Problem 97

Ella's race time, assuming she took 5 sec longer than Kyle and Kyle took 3 sec longer than Amy. Assume that Amy's time was $t$ seconds.

Quinn Langford

Numerade Educator

01:23

Problem 98

Ray's age 7 years from now if he is 2 years older than Monique and Monique is a years old

Veronica Santana

Numerade Educator

01:42

Problem 99

If the height of a triangle is doubled, is its area also Houbled? Why or why not?

Quinn Langford

Numerade Educator

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