Elementary and Intermediate Algebra

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

Chapter 2

Equations, Inequalities, and Problem Solving

Educators

SA

Problem 1

Match the statement with the most appropriate choice from the column on the right.
The equations $x+3=7$ and $6 x=24$
a) Coefficient
b) Equivalent expressions
c) Equivalent equations
d) The multiplication principle
e) The addition principle
f) Solution

SA
Sheila A.
Numerade Educator

Problem 2

Match the statement with the most appropriate choice from the column on the right.
The expressions $3(x-2)$ and $3 x-6$
a) Coefficient
b) Equivalent expressions
c) Equivalent equations
d) The multiplication principle
e) The addition principle
f) Solution

Joshua F.
Numerade Educator

Problem 3

Match the statement with the most appropriate choice from the column on the right.
A replacement that makes an equation true
a) Coefficient
b) Equivalent expressions
c) Equivalent equations
d) The multiplication principle
e) The addition principle
f) Solution

SA
Sheila A.
Numerade Educator

Problem 4

Match the statement with the most appropriate choice from the column on the right.
The role of 9 in $9 a b$
a) Coefficient
b) Equivalent expressions
c) Equivalent equations
d) The multiplication principle
e) The addition principle
f) Solution

Joshua F.
Numerade Educator

Problem 5

Match the statement with the most appropriate choice from the column on the right.
The principle used to solve $\frac{2}{3} \cdot x=-4 \quad$
a) Coefficient
b) Equivalent expressions
c) Equivalent equations
d) The multiplication principle
e) The addition principle
f) Solution

SA
Sheila A.
Numerade Educator

Problem 6

Match the statement with the most appropriate choice from the column on the right.
The principle used to solve $\frac{2}{3}+x=-4 \quad$
a) Coefficient
b) Equivalent expressions
c) Equivalent equations
d) The multiplication principle
e) The addition principle
f) Solution

Joshua F.
Numerade Educator

Problem 7

Match the equation with the step, from the column on the right, that would be used to solve the equation.
$6 x=30$
a) Add 6 to both sides.
b) Subtract 6 from both sides.
c) Multiply both sides by $6 .$
d) Divide both sides by 6

SA
Sheila A.
Numerade Educator

Problem 8

Match the equation with the step, from the column on the right, that would be used to solve the equation.
$x+6=30 \quad$
a) Add 6 to both sides.
b) Subtract 6 from both sides.
c) Multiply both sides by $6 .$
d) Divide both sides by 6

Joshua F.
Numerade Educator

Problem 9

Match the equation with the step, from the column on the right, that would be used to solve the equation.
$\frac{1}{6} x=30 \quad$
a) Add 6 to both sides.
b) Subtract 6 from both sides.
c) Multiply both sides by $6 .$
d) Divide both sides by 6

SA
Sheila A.
Numerade Educator

Problem 10

Match the equation with the step, from the column on the right, that would be used to solve the equation.
$x-6=30 \quad$
a) Add 6 to both sides.
b) Subtract 6 from both sides.
c) Multiply both sides by $6 .$
d) Divide both sides by 6

Joshua F.
Numerade Educator

Problem 11

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.

Determine whether the given number is a solution of the given equation.
$$
6-x=-2 ; 4
$$

SA
Sheila A.
Numerade Educator

Problem 12

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.

Determine whether the given number is a solution of the given equation.
$$
6-x=-2 ; 8
$$

Joshua F.
Numerade Educator

Problem 13

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.

Determine whether the given number is a solution of the given equation.
$$
\frac{2}{3} t=12 ; 18
$$

SA
Sheila A.
Numerade Educator

Problem 14

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.

Determine whether the given number is a solution of the given equation.
$$
\frac{2}{3} t=12 ; 8
$$

Joshua F.
Numerade Educator

Problem 15

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.

Determine whether the given number is a solution of the given equation.
$$
x+7=3-x ;-2
$$

SA
Sheila A.
Numerade Educator

Problem 16

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.

Determine whether the given number is a solution of the given equation.
$$
-4+x=5 x ;-1
$$

Joshua F.
Numerade Educator

Problem 17

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.

Determine whether the given number is a solution of the given equation.
$$
4-\frac{1}{5} n=8 ;-20
$$

SA
Sheila A.
Numerade Educator

Problem 18

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.

Determine whether the given number is a solution of the given equation.
$$
-3=5-\frac{n}{2} ; 4
$$

Joshua F.
Numerade Educator

Problem 19

Solve using the addition principle. Don't forget to check!

SA
Sheila A.
Numerade Educator

Problem 20

Solve using the addition principle. Don't forget to check!
$$
x+5=8
$$

Joshua F.
Numerade Educator

Problem 21

Solve using the addition principle. Don't forget to check!
$$
y+7=-4
$$

SA
Sheila A.
Numerade Educator

Problem 22

Solve using the addition principle. Don't forget to check!
$$
t+6=43
$$

Joshua F.
Numerade Educator

Problem 23

Solve using the addition principle. Don't forget to check!
$$
-6=y+25
$$

SA
Sheila A.
Numerade Educator

Problem 24

Solve using the addition principle. Don't forget to check!
$$
-5=x+8
$$

Joshua F.
Numerade Educator

Problem 25

Solve using the addition principle. Don't forget to check!
$$
x-8=5
$$

SA
Sheila A.
Numerade Educator

Problem 26

Solve using the addition principle. Don't forget to check!
$$
x-9=6
$$

Joshua F.
Numerade Educator

Problem 27

Solve using the addition principle. Don't forget to check!
$$
12=-7+y
$$

SA
Sheila A.
Numerade Educator

Problem 28

Solve using the addition principle. Don't forget to check!
$$
15=-8+z
$$

Joshua F.
Numerade Educator

Problem 29

Solve using the addition principle. Don't forget to check!
$$
-5+t=-9
$$

SA
Sheila A.
Numerade Educator

Problem 30

Solve using the addition principle. Don't forget to check!
$$
-6+y=-21
$$

Joshua F.
Numerade Educator

Problem 31

Solve using the addition principle. Don't forget to check!
$$
r+\frac{1}{3}=\frac{8}{3}
$$

SA
Sheila A.
Numerade Educator

Problem 32

Solve using the addition principle. Don't forget to check!
$$
t+\frac{3}{8}=\frac{5}{8}
$$

Joshua F.
Numerade Educator

Problem 33

Solve using the addition principle. Don't forget to check!
$$
x-\frac{3}{5}=-\frac{7}{10}
$$

SA
Sheila A.
Numerade Educator

Problem 34

Solve using the addition principle. Don't forget to check!
$$
x-\frac{2}{3}=-\frac{5}{6}
$$

Joshua F.
Numerade Educator

Problem 35

Solve using the addition principle. Don't forget to check!
$$
-\frac{1}{5}+z=-\frac{1}{4}
$$

SA
Sheila A.
Numerade Educator

Problem 36

Solve using the addition principle. Don't forget to check!
$$
-\frac{1}{8}+y=-\frac{3}{4}
$$

Joshua F.
Numerade Educator

Problem 37

Solve using the addition principle. Don't forget to check!
$$
m+3.9=5.4
$$

SA
Sheila A.
Numerade Educator

Problem 38

Solve using the addition principle. Don't forget to check!
$$
y+5.3=8.7
$$

Joshua F.
Numerade Educator

Problem 39

Solve using the addition principle. Don't forget to check!
$$
-9.7=-4.7+y
$$

SA
Sheila A.
Numerade Educator

Problem 40

Solve using the addition principle. Don't forget to check!
$$
-7.8=2.8+x
$$

Joshua F.
Numerade Educator

Problem 41

Solve using the multiplication principle. Don't forget to check!
$$
5 x=70
$$

SA
Sheila A.
Numerade Educator

Problem 42

Solve using the multiplication principle. Don't forget to check!
$$
3 x=39
$$

Joshua F.
Numerade Educator

Problem 43

Solve using the multiplication principle. Don't forget to check!
$$
84=7 n
$$

SA
Sheila A.
Numerade Educator

Problem 44

Solve using the multiplication principle. Don't forget to check!
$$
56=7 t
$$

Joshua F.
Numerade Educator

Problem 45

Solve using the multiplication principle. Don't forget to check!
$$
-x=23
$$

SA
Sheila A.
Numerade Educator

Problem 46

Solve using the multiplication principle. Don't forget to check!
$$
100=-x
$$

Joshua F.
Numerade Educator

Problem 47

Solve using the multiplication principle. Don't forget to check!
$$
-t=-8
$$

SA
Sheila A.
Numerade Educator

Problem 48

Solve using the multiplication principle. Don't forget to check!
$$
-68=-r
$$

Joshua F.
Numerade Educator

Problem 49

Solve using the multiplication principle. Don't forget to check!
$$
2 x=-5
$$

SA
Sheila A.
Numerade Educator

Problem 50

Solve using the multiplication principle. Don't forget to check!
$$
-3 x=5
$$

Joshua F.
Numerade Educator

Problem 51

Solve using the multiplication principle. Don't forget to check!
$$
-1.3 a=-10.4
$$

SA
Sheila A.
Numerade Educator

Problem 52

Solve using the multiplication principle. Don't forget to check!
$$
-3.4 t=-20.4
$$

Joshua F.
Numerade Educator

Problem 53

Solve using the multiplication principle. Don't forget to check!
$$
\frac{y}{-8}=11
$$

SA
Sheila A.
Numerade Educator

Problem 54

Solve using the multiplication principle. Don't forget to check!
$$
\frac{a}{4}=13
$$

Joshua F.
Numerade Educator

Problem 55

Solve using the multiplication principle. Don't forget to check!
$$
\frac{4}{5} x=16
$$

SA
Sheila A.
Numerade Educator

Problem 56

Solve using the multiplication principle. Don't forget to check!
$$
\frac{3}{4} x=27
$$

Joshua F.
Numerade Educator

Problem 57

Solve using the multiplication principle. Don't forget to check!
$$
\frac{-x}{6}=9
$$

SA
Sheila A.
Numerade Educator

Problem 58

Solve using the multiplication principle. Don't forget to check!
$$
\frac{-t}{5}=9
$$

Joshua F.
Numerade Educator

Problem 59

Solve using the multiplication principle. Don't forget to check!
$$
\frac{1}{9}=\frac{z}{5}
$$

SA
Sheila A.
Numerade Educator

Problem 60

Solve using the multiplication principle. Don't forget to check!
$$
\frac{2}{7}=\frac{x}{3}
$$

Joshua F.
Numerade Educator

Problem 61

Solve using the multiplication principle. Don't forget to check!
$$
-\frac{3}{5} r=-\frac{3}{5}
$$

SA
Sheila A.
Numerade Educator

Problem 62

Solve using the multiplication principle. Don't forget to check!
$$
-\frac{2}{5} y=-\frac{4}{15}
$$

Joshua F.
Numerade Educator

Problem 63

Solve using the multiplication principle. Don't forget to check!
$$
\frac{-3 r}{2}=-\frac{27}{4}
$$

SA
Sheila A.
Numerade Educator

Problem 64

Solve using the multiplication principle. Don't forget to check!
$$
\frac{5 x}{7}=-\frac{10}{14}
$$

Joshua F.
Numerade Educator

Problem 65

Solve. The symbol indicates an exercise designed to give practice using a calculator.
$$
4.5+t=-3.1
$$

SA
Sheila A.
Numerade Educator

Problem 66

Solve. The symbol indicates an exercise designed to give practice using a calculator.
$$
\frac{3}{4} x=18
$$

Joshua F.
Numerade Educator

Problem 67

Solve. The symbol indicates an exercise designed to give practice using a calculator.
$$
\frac{3}{4} x=18
$$

SA
Sheila A.
Numerade Educator

Problem 68

Solve. The symbol indicates an exercise designed to give practice using a calculator.
$$
t-7.4=-12.9
$$

Joshua F.
Numerade Educator

Problem 69

Solve. The symbol indicates an exercise designed to give practice using a calculator.
$$
x-4=-19
$$

SA
Sheila A.
Numerade Educator

Problem 70

Solve. The symbol indicates an exercise designed to give practice using a calculator.
$$
y-6=-14
$$

Joshua F.
Numerade Educator

Problem 71

Solve. The symbol indicates an exercise designed to give practice using a calculator.
$$
-12 x=72
$$

SA
Sheila A.
Numerade Educator

Problem 72

Solve. The symbol indicates an exercise designed to give practice using a calculator.
$$
-15 x=105
$$

Joshua F.
Numerade Educator

Problem 73

Solve. The symbol indicates an exercise designed to give practice using a calculator.
$$
48=-\frac{3}{8} y
$$

SA
Sheila A.
Numerade Educator

Problem 74

Solve. The symbol indicates an exercise designed to give practice using a calculator.
$$
14=t+27
$$

Joshua F.
Numerade Educator

Problem 75

Solve. The symbol indicates an exercise designed to give practice using a calculator.
$$
a-\frac{1}{6}=-\frac{2}{3}
$$

SA
Sheila A.
Numerade Educator

Problem 76

Solve. The symbol indicates an exercise designed to give practice using a calculator.
$$
-\frac{x}{7}=\frac{2}{9}
$$

Joshua F.
Numerade Educator

Problem 77

Solve. The symbol indicates an exercise designed to give practice using a calculator.
$$
-24=\frac{8 x}{5}
$$

SA
Sheila A.
Numerade Educator

Problem 78

Solve. The symbol indicates an exercise designed to give practice using a calculator.
$$
\frac{1}{5}+y=-\frac{3}{10}
$$

Joshua F.
Numerade Educator

Problem 79

Solve. The symbol indicates an exercise designed to give practice using a calculator.
$$
-\frac{4}{3} t=-16
$$

SA
Sheila A.
Numerade Educator

Problem 80

Solve. The symbol indicates an exercise designed to give practice using a calculator.
$$
\frac{17}{35}=-x
$$

Joshua F.
Numerade Educator

Problem 81

Solve. The symbol indicates an exercise designed to give practice using a calculator.
$$
-483.297=-794.053+t
$$

SA
Sheila A.
Numerade Educator

Problem 82

Solve. The symbol indicates an exercise designed to give practice using a calculator.
$$
-0.2344 x=2028.732
$$

Joshua F.
Numerade Educator

Problem 83

When solving an equation, how do you determine what number to add, subtract, multiply, or divide by on both sides of that equation?

SA
Sheila A.
Numerade Educator

Problem 84

What is the difference between equivalent expressions and equivalent equations?

Joshua F.
Numerade Educator

Problem 85

To prepare for Section $2.2,$ review the rules for order of operations (Section $1.8)$
Simplify. [ 1.8]
$$
3 \cdot 4-18
$$

SA
Sheila A.
Numerade Educator

Problem 86

To prepare for Section $2.2,$ review the rules for order of operations (Section $1.8)$
Simplify. [ 1.8]
$$
14-2(7-1)
$$

Joshua F.
Numerade Educator

Problem 87

To prepare for Section $2.2,$ review the rules for order of operations (Section $1.8)$
Simplify. [ 1.8]
$$
16 \div(2-3 \cdot 2)+5
$$

SA
Sheila A.
Numerade Educator

Problem 88

To prepare for Section $2.2,$ review the rules for order of operations (Section $1.8)$
Simplify. [ 1.8]
$$
12-5 \cdot 2^{3}+4 \cdot 3
$$

Joshua F.
Numerade Educator

Problem 89

To solve $-3.5=14 t,$ Gregory adds 3.5 to both sides. Will this form an equivalent equation? Will it help solve the equation? Explain.

SA
Sheila A.
Numerade Educator

Problem 90

Explain why it is not necessary to state a subtraction principle: For any real numbers $a, b,$ and $c, a=b$ is equivalent to $a-c=b-c$

Joshua F.
Numerade Educator

Problem 91

Solve for $x .$ Assume $a, c, m \neq 0$
$$
m x=9.4 m
$$

SA
Sheila A.
Numerade Educator

Problem 92

Solve for $x .$ Assume $a, c, m \neq 0$
$$
x-4+a=a
$$

Joshua F.
Numerade Educator

Problem 93

Solve for $x .$ Assume $a, c, m \neq 0$
$$
c x+5 c=7 c
$$

SA
Sheila A.
Numerade Educator

Problem 94

Solve for $x .$ Assume $a, c, m \neq 0$
$$
c \cdot \frac{21}{a}=\frac{7 c x}{2 a}
$$

Joshua F.
Numerade Educator

Problem 95

Solve for $x .$ Assume $a, c, m \neq 0$
$$
7+|x|=20
$$

SA
Sheila A.
Numerade Educator

Problem 96

Solve for $x .$ Assume $a, c, m \neq 0$
$$
a x-3 a=5 a
$$

Joshua F.
Numerade Educator

Problem 97

Solve for $x .$ Assume $a, c, m \neq 0$
$$
\text { If } t-3590=1820, \text { find } t+3590
$$

SA
Sheila A.
Numerade Educator

Problem 98

Solve for $x .$ Assume $a, c, m \neq 0$
$$
\text { If } n+268=124, \text { find } n-268
$$

Joshua F.
Numerade Educator

Problem 99

Alayna makes a calculation and gets an answer of $22.5 .$ On the last step, she multiplies by 0.3 when she should have divided by 0.3. What is the correct answer?

SA
Sheila A.
Numerade Educator

Problem 100

Are the equations $x=5$ and $x^{2}=25$ equivalent? Why or why not?

Joshua F.
Numerade Educator