# Elementary and Intermediate Algebra

## 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### Problem 19

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

SA
Sheila A.

### Problem 20

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

Joshua F.

### Problem 21

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

SA
Sheila A.

### Problem 22

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

Joshua F.

### Problem 23

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

SA
Sheila A.

### Problem 24

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

Joshua F.

### Problem 25

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

SA
Sheila A.

### Problem 26

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

Joshua F.

### Problem 27

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

SA
Sheila A.

### Problem 28

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

Joshua F.

### Problem 29

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

SA
Sheila A.

### Problem 30

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

Joshua F.

### Problem 31

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

SA
Sheila A.

### Problem 32

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

Joshua F.

### Problem 33

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

SA
Sheila A.

### Problem 34

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

Joshua F.

### Problem 35

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

SA
Sheila A.

### Problem 36

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

Joshua F.

### Problem 37

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

SA
Sheila A.

### Problem 38

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

Joshua F.

### Problem 39

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

SA
Sheila A.

### Problem 40

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

Joshua F.

### Problem 41

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

SA
Sheila A.

### Problem 42

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

Joshua F.

### Problem 43

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

SA
Sheila A.

### Problem 44

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

Joshua F.

### Problem 45

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

SA
Sheila A.

### Problem 46

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

Joshua F.

### Problem 47

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

SA
Sheila A.

### Problem 48

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

Joshua F.

### Problem 49

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

SA
Sheila A.

### Problem 50

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

Joshua F.

### Problem 51

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

SA
Sheila A.

### Problem 52

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

Joshua F.

### Problem 53

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

SA
Sheila A.

### Problem 54

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

Joshua F.

### Problem 55

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

SA
Sheila A.

### Problem 56

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

Joshua F.

### Problem 57

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

SA
Sheila A.

### Problem 58

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

Joshua F.

### Problem 59

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

SA
Sheila A.

### Problem 60

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

Joshua F.

### Problem 61

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

SA
Sheila A.

### Problem 62

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

Joshua F.

### Problem 63

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

SA
Sheila A.

### Problem 64

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

Joshua F.

### Problem 65

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

SA
Sheila A.

### Problem 66

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

Joshua F.

### Problem 67

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

SA
Sheila A.

### Problem 68

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

Joshua F.

### Problem 69

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

SA
Sheila A.

### Problem 70

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

Joshua F.

### Problem 71

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

SA
Sheila A.

### Problem 72

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

Joshua F.

### Problem 73

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

SA
Sheila A.

### Problem 74

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

Joshua F.

### 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.

### Problem 76

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

Joshua F.

### Problem 77

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

SA
Sheila A.

### Problem 78

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

Joshua F.

### Problem 79

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

SA
Sheila A.

### Problem 80

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

Joshua F.

### Problem 81

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

SA
Sheila A.

### Problem 82

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

Joshua F.

### 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.

### Problem 84

What is the difference between equivalent expressions and equivalent equations?

Joshua F.

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### Problem 91

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

SA
Sheila A.

### Problem 92

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

Joshua F.

### Problem 93

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

SA
Sheila A.

### Problem 94

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

Joshua F.

### Problem 95

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

SA
Sheila A.

### Problem 96

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

Joshua F.

### Problem 97

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

SA
Sheila A.

### Problem 98

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

Joshua F.

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