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  • Elementary and Intermediate Algebra 5th
  • Equations, Inequalities, and Problem Solving

Elementary and Intermediate Algebra 5th

Alan S. Tussy, R. David Gustafson

Chapter 2

Equations, Inequalities, and Problem Solving - all with Video Answers

Educators

Section 1

Solving Equations Using Properties of Equality

00:12

Problem 1

Fill in the blanks.
A statement indicating that two expressions are equal, such as $x+1=7,$ is called an____________

Melissa S.
Melissa S.
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00:14

Problem 2

Fill in the blanks.
Any number that makes an equation true when substituted for the variable is said to ___________ the equation. Such numbers are called__________

Melissa S.
Melissa S.
Numerade Educator
00:06

Problem 3

Fill in the blanks.
To______________an equation means to find all values of the variable that make the equation true.

Melissa S.
Melissa S.
Numerade Educator
00:07

Problem 4

Fill in the blanks.
To solve an equation, we_______________ the variable on one side of the equation.

Melissa S.
Melissa S.
Numerade Educator
00:08

Problem 5

Fill in the blanks.
Equations with the same solutions are called___________________equations.

Melissa S.
Melissa S.
Numerade Educator
00:10

Problem 6

Fill in the blanks.
To________________the solution of an equation, we substitute the value for the variable in the original equation and determine whether the result is a true statement.

Melissa S.
Melissa S.
Numerade Educator
00:43

Problem 7

Given $x+6=12$
a. What is the left side of the equation?
b. Is this equation true, false, or neither?
c. Is 5 the solution?
d. Does 6 satisfy the equation?

Melissa S.
Melissa S.
Numerade Educator
01:01

Problem 8

For each equation, determine what operation is performed on the variable. Then explain how to undo that operation to isolate the variable.
a. $x-8=24$
b. $x+8=24$
c. $\frac{x}{8}=24$
d. $8 x=24$

Melissa S.
Melissa S.
Numerade Educator
00:21

Problem 9

Complete the following properties of equality. If $a=b$, then
a. $a+c=b+\quad$ and $\quad a-c=b-$
b. $\quad c a=\quad b$
and $\quad \frac{a}{c}=\frac{b}{(\text { where } c \neq 0)}$

Melissa S.
Melissa S.
Numerade Educator
00:17

Problem 10

a. To solve $\frac{h}{10}=20,$ do we multiply both sides of the equation by 10 or $20 ?$
b. To solve $4 k=16,$ do we subtract 4 from both sides of the equation or divide both sides by 4?

Melissa S.
Melissa S.
Numerade Educator
00:41

Problem 11

Simplify each expression.
a. $x+7-7$
b. $y-2+2$
c. $\frac{5 t}{5}$
d. $6 \cdot \frac{h}{6}$

Melissa S.
Melissa S.
Numerade Educator
00:18

Problem 12

a. To solve $-\frac{4}{5} x=8,$ we can multiply both sides by the reciprocal of $-\frac{4}{5} .$ What is the reciprocal of $-\frac{4}{5} ?$
b. What is $-\frac{5}{4}\left(-\frac{4}{5}\right) ?$

Melissa S.
Melissa S.
Numerade Educator
00:39

Problem 13

Complete each solution to solve the equation.
$$
\begin{aligned}
x-5 &=45 \\
x-5+&=45+\\
x &=
\end{aligned}
$$
Check: $\quad x-5=45$
$$
\begin{aligned}-5 &=45 \\ &=45 \end{aligned}
$$
is the solution.

Melissa S.
Melissa S.
Numerade Educator
00:36

Problem 14

Complete each solution to solve the equation.
$$
\begin{aligned}
&8 x=40\\
&\frac{8 x}{2}=\frac{40}{1}\\
&x=
\end{aligned}
$$
Check: $\quad 8 x=40$
()$8=40$
$$
=40 \quad \text { True }
$$
is the solution.

Melissa S.
Melissa S.
Numerade Educator
00:27

Problem 15

Complete each solution to solve the equation.
a. What does the symbol $\stackrel{7}{=}$ mean?
b. If you solve an equation and obtain $50=x,$ can you write $x=50 ?$

Melissa S.
Melissa S.
Numerade Educator
00:05

Problem 16

Complete each solution to solve the equation.
Fill in the blank: $-x=$

Melissa S.
Melissa S.
Numerade Educator
00:17

Problem 17

Check to determine whether the number in red is a solution of the equation. See Example $1 .$
$$
6, x+12=28
$$

Melissa S.
Melissa S.
Numerade Educator
00:17

Problem 18

Check to determine whether the number in red is a solution of the equation. See Example $1 .$
$$
110, x-50=60
$$

Melissa S.
Melissa S.
Numerade Educator
00:28

Problem 19

Check to determine whether the number in red is a solution of the equation. See Example $1 .$
$$
-8,2 b+3=-15
$$

Melissa S.
Melissa S.
Numerade Educator
00:26

Problem 20

Check to determine whether the number in red is a solution of the equation. See Example $1 .$
$$
-2,5 t-4=-16
$$

Melissa S.
Melissa S.
Numerade Educator
00:22

Problem 21

Check to determine whether the number in red is a solution of the equation. See Example $1 .$
$$
5,0.5 x=2.9
$$

Melissa S.
Melissa S.
Numerade Educator
00:25

Problem 22

Check to determine whether the number in red is a solution of the equation. See Example $1 .$
$$
3.5,1.2+x=4.7
$$

Melissa S.
Melissa S.
Numerade Educator
00:40

Problem 23

Check to determine whether the number in red is a solution of the equation. See Example $1 .$
$$
-6,33-\frac{x}{2}=30
$$

Melissa S.
Melissa S.
Numerade Educator
00:28

Problem 24

Check to determine whether the number in red is a solution of the equation. See Example $1 .$
$$
-8, \frac{x}{4}+98=100
$$

Melissa S.
Melissa S.
Numerade Educator
00:27

Problem 25

Check to determine whether the number in red is a solution of the equation. See Example $1 .$
$$
-2,|c-8|=10
$$

Melissa S.
Melissa S.
Numerade Educator
00:37

Problem 26

Check to determine whether the number in red is a solution of the equation. See Example $1 .$
$$
-45, \quad|30-r|=15
$$

Melissa S.
Melissa S.
Numerade Educator
00:43

Problem 27

Check to determine whether the number in red is a solution of the equation. See Example $1 .$
$$
12,3 x-2=4 x-5
$$

Melissa S.
Melissa S.
Numerade Educator
00:41

Problem 28

Check to determine whether the number in red is a solution of the equation. See Example $1 .$
$$
5,5 y+8=3 y-2
$$

Melissa S.
Melissa S.
Numerade Educator
00:38

Problem 29

Check to determine whether the number in red is a solution of the equation. See Example $1 .$
$$
-3, x^{2}-x-6=0
$$

Melissa S.
Melissa S.
Numerade Educator
00:37

Problem 30

Check to determine whether the number in red is a solution of the equation. See Example $1 .$
$$
-2, y^{2}+5 y-3=0
$$

Melissa S.
Melissa S.
Numerade Educator
00:48

Problem 31

Check to determine whether the number in red is a solution of the equation. See Example $1 .$
$$
\text { 1, } \frac{2}{a+1}+5=\frac{12}{a+1}
$$

Melissa S.
Melissa S.
Numerade Educator
00:54

Problem 32

Check to determine whether the number in red is a solution of the equation. See Example $1 .$
$$
\text { 4, } \frac{2 t}{t-2}-\frac{4}{t-2}=1
$$

Melissa S.
Melissa S.
Numerade Educator
00:40

Problem 33

Check to determine whether the number in red is a solution of the equation. See Example $1 .$
$$
\frac{3}{4}, x-\frac{1}{8}=\frac{5}{8}
$$

Melissa S.
Melissa S.
Numerade Educator
00:33

Problem 34

Check to determine whether the number in red is a solution of the equation. See Example $1 .$
$$
\frac{7}{3},-4=a+\frac{5}{3}
$$

Melissa S.
Melissa S.
Numerade Educator
00:39

Problem 35

Check to determine whether the number in red is a solution of the equation. See Example $1 .$
$$
-3,(x-4)(x+3)=0
$$

Melissa S.
Melissa S.
Numerade Educator
00:41

Problem 36

Check to determine whether the number in red is a solution of the equation. See Example $1 .$
$$
5,(2 x+1)(x-5)=0
$$

Melissa S.
Melissa S.
Numerade Educator
00:31

Problem 37

Use a property of equality to solve each equation. Then check the result. See Example $2 .$
$$
a-5=66
$$

Melissa S.
Melissa S.
Numerade Educator
00:34

Problem 38

Use a property of equality to solve each equation. Then check the result. See Example $2 .$
$$
x-34=19
$$

Melissa S.
Melissa S.
Numerade Educator
00:35

Problem 39

Use a property of equality to solve each equation. Then check the result. See Example $2 .$
$$
9=p-9
$$

Melissa S.
Melissa S.
Numerade Educator
00:38

Problem 40

Use a property of equality to solve each equation. Then check the result. See Example $2 .$
$$
3=j-88
$$

Melissa S.
Melissa S.
Numerade Educator
00:35

Problem 41

Use a property of equality to solve each equation. Then check the result. See Example $3 .$
$$
-16=y-4
$$

Melissa S.
Melissa S.
Numerade Educator
00:39

Problem 42

Use a property of equality to solve each equation. Then check the result. See Example $3 .$
$$
-23=y-19
$$

Melissa S.
Melissa S.
Numerade Educator
00:35

Problem 43

Use a property of equality to solve each equation. Then check the result. See Example $3 .$
$$
-3+a=0
$$

Melissa S.
Melissa S.
Numerade Educator
00:33

Problem 44

Use a property of equality to solve each equation. Then check the result. See Example $3 .$
$$
-1+m=0
$$

Melissa S.
Melissa S.
Numerade Educator
01:04

Problem 45

Use a property of equality to solve each equation. Then check the result. See Example $3 .$
$$
x+\frac{1}{10}=\frac{6}{5}
$$

Melissa S.
Melissa S.
Numerade Educator
00:59

Problem 46

Use a property of equality to solve each equation. Then check the result. See Example $3 .$
$$
x+\frac{1}{14}=\frac{9}{7}
$$

Melissa S.
Melissa S.
Numerade Educator
00:46

Problem 47

Use a property of equality to solve each equation. Then check the result. See Example $3 .$
$$
3.5+f=1.2
$$

Melissa S.
Melissa S.
Numerade Educator
00:47

Problem 48

Use a property of equality to solve each equation. Then check the result. See Example 4.
$$
9.4+h=8.1
$$

Melissa S.
Melissa S.
Numerade Educator
00:36

Problem 49

Use a property of equality to solve each equation. Then check the result. See Example $5 .$
$$
\frac{x}{15}=3
$$

Melissa S.
Melissa S.
Numerade Educator
00:36

Problem 50

Use a property of equality to solve each equation. Then check the result. See Example $5 .$
$$
\frac{y}{7}=12
$$

Melissa S.
Melissa S.
Numerade Educator
00:44

Problem 51

Use a property of equality to solve each equation. Then check the result. See Example $5 .$
$$
\frac{d}{8}=-6
$$

Melissa S.
Melissa S.
Numerade Educator
00:39

Problem 52

Use a property of equality to solve each equation. Then check the result. See Example $5 .$
$$
\frac{n}{9}=-2
$$

Melissa S.
Melissa S.
Numerade Educator
00:51

Problem 53

Use a property of equality to solve each equation. Then check the result. See Example 6
$$
\frac{4}{5} t=16
$$

Melissa S.
Melissa S.
Numerade Educator
01:05

Problem 54

Use a property of equality to solve each equation. Then check the result. See Example 6
$$
\frac{11}{15} y=22
$$

Melissa S.
Melissa S.
Numerade Educator
01:29

Problem 55

Use a property of equality to solve each equation. Then check the result. See Example 6
$$
-\frac{7 r}{2}=\frac{5}{12}
$$

Melissa S.
Melissa S.
Numerade Educator
01:53

Problem 56

Use a property of equality to solve each equation. Then check the result. See Example 6
$$
-\frac{4 a}{5}=\frac{11}{15}
$$

Melissa S.
Melissa S.
Numerade Educator
00:33

Problem 57

Use a property of equality to solve each equation. Then check the result. See Example 7 .
$$
4 x=16
$$

Melissa S.
Melissa S.
Numerade Educator
00:36

Problem 58

Use a property of equality to solve each equation. Then check the result. See Example 7 .
$$
5 y=45
$$

Melissa S.
Melissa S.
Numerade Educator
00:49

Problem 59

Use a property of equality to solve each equation. Then check the result. See Example 7 .
$$
-1.7=-3.4 y
$$

Melissa S.
Melissa S.
Numerade Educator
00:52

Problem 60

Use a property of equality to solve each equation. Then check the result. See Example 7 .
$$
-1.26=-2.1 x
$$

Melissa S.
Melissa S.
Numerade Educator
00:37

Problem 61

Use a property of equality to solve each equation. Then check the result. See Example 8 .
$$
-x=18
$$

Melissa S.
Melissa S.
Numerade Educator
00:43

Problem 62

Use a property of equality to solve each equation. Then check the result. See Example 8 .
$$
-y=50
$$

Melissa S.
Melissa S.
Numerade Educator
00:45

Problem 63

Use a property of equality to solve each equation. Then check the result. See Example 8 .
$$
-n=\frac{4}{21}
$$

Melissa S.
Melissa S.
Numerade Educator
00:48

Problem 64

Use a property of equality to solve each equation. Then check the result. See Example 8 .
$$
-w=\frac{11}{16}
$$

Melissa S.
Melissa S.
Numerade Educator
00:39

Problem 65

Solve each equation. Then check the result.
$$
63=9 c
$$

Melissa S.
Melissa S.
Numerade Educator
00:36

Problem 66

Solve each equation. Then check the result.
$$
40=5 t
$$

Melissa S.
Melissa S.
Numerade Educator
00:46

Problem 67

Solve each equation. Then check the result.
$$
d-\frac{1}{9}=\frac{7}{9}
$$

Melissa S.
Melissa S.
Numerade Educator
00:53

Problem 68

Solve each equation. Then check the result.
$$
\frac{7}{15}=b-\frac{1}{15}
$$

Melissa S.
Melissa S.
Numerade Educator
00:45

Problem 69

Solve each equation. Then check the result.
$$
0=\frac{v}{11}
$$

Melissa S.
Melissa S.
Numerade Educator
00:41

Problem 70

Solve each equation. Then check the result.
$$
\frac{d}{49}=0
$$

Melissa S.
Melissa S.
Numerade Educator
00:55

Problem 71

Solve each equation. Then check the result.
$$
x-1.6=-2.5
$$

Melissa S.
Melissa S.
Numerade Educator
00:54

Problem 72

Solve each equation. Then check the result.
$$
y-1.2=-1.3
$$

Melissa S.
Melissa S.
Numerade Educator
00:55

Problem 73

Solve each equation. Then check the result.
$$
\frac{2}{3} c=10
$$

Melissa S.
Melissa S.
Numerade Educator
01:01

Problem 74

Solve each equation. Then check the result.
$$
\frac{9}{7} d=81
$$

Melissa S.
Melissa S.
Numerade Educator
00:45

Problem 75

Solve each equation. Then check the result.
$$
-100=-5 g
$$

Melissa S.
Melissa S.
Numerade Educator
00:42

Problem 76

Solve each equation. Then check the result.
$$
-80=-5 w
$$

Melissa S.
Melissa S.
Numerade Educator
01:21

Problem 77

Solve each equation. Then check the result.
$$
s+\frac{1}{5}=\frac{4}{25}
$$

Melissa S.
Melissa S.
Numerade Educator
01:12

Problem 78

Solve each equation. Then check the result.
$$
\frac{1}{6}=h+\frac{4}{3}
$$

Melissa S.
Melissa S.
Numerade Educator
00:43

Problem 79

Solve each equation. Then check the result.
$$
\frac{d}{-7}=-3
$$

Melissa S.
Melissa S.
Numerade Educator
00:46

Problem 80

Solve each equation. Then check the result.
$$
\frac{c}{-2}=-11
$$

Melissa S.
Melissa S.
Numerade Educator
00:36

Problem 81

Solve each equation. Then check the result.
$$
8 h=0
$$

Melissa S.
Melissa S.
Numerade Educator
00:38

Problem 82

Solve each equation. Then check the result.
$$
9 a=0
$$

Melissa S.
Melissa S.
Numerade Educator
00:57

Problem 83

Solve each equation. Then check the result.
$$
\frac{y}{0.6}=-4.4
$$

Melissa S.
Melissa S.
Numerade Educator
01:00

Problem 84

Solve each equation. Then check the result.
$$
\frac{y}{0.8}=-2.9
$$

Melissa S.
Melissa S.
Numerade Educator
00:34

Problem 85

Solve each equation. Then check the result.
$$
23 b=23
$$

Melissa S.
Melissa S.
Numerade Educator
00:37

Problem 86

Solve each equation. Then check the result.
$$
16=16 h
$$

Melissa S.
Melissa S.
Numerade Educator
00:52

Problem 87

Solve each equation. Then check the result.
$$
-\frac{5}{4} h=-5
$$

Melissa S.
Melissa S.
Numerade Educator
00:54

Problem 88

Solve each equation. Then check the result.
$$
-\frac{3}{8} t=-3
$$

Melissa S.
Melissa S.
Numerade Educator
00:46

Problem 89

Solve each equation. Then check the result.
$$
8.9=-4.1+t
$$

Melissa S.
Melissa S.
Numerade Educator
00:48

Problem 90

Solve each equation. Then check the result.
$$
7.7=-3.2+s
$$

Melissa S.
Melissa S.
Numerade Educator
00:34

Problem 91

Solve each equation. Then check the result.
$$
-2.5=-m
$$

Melissa S.
Melissa S.
Numerade Educator
00:36

Problem 92

Solve each equation. Then check the result.
$$
-1.8=-b
$$

Melissa S.
Melissa S.
Numerade Educator
01:12

Problem 93

Solve each equation. Then check the result.
$$
-\frac{9}{8} x=3
$$

Melissa S.
Melissa S.
Numerade Educator
01:06

Problem 94

Solve each equation. Then check the result.
$$
-\frac{14}{3} c=7
$$

Melissa S.
Melissa S.
Numerade Educator
01:12

Problem 95

Solve each equation. Then check the result.
$$
\frac{2}{3} n=-\frac{7}{8}
$$

Melissa S.
Melissa S.
Numerade Educator
01:30

Problem 96

Solve each equation. Then check the result.
$$
\frac{4}{9} m=-\frac{3}{5}
$$

Melissa S.
Melissa S.
Numerade Educator
00:40

Problem 97

Solve each equation. Then check the result.
$$
-10=n-5
$$

Melissa S.
Melissa S.
Numerade Educator
00:41

Problem 98

Solve each equation. Then check the result.
$$
-8=t-2
$$

Melissa S.
Melissa S.
Numerade Educator
00:47

Problem 99

Solve each equation. Then check the result.
$$
\frac{h}{-40}=5
$$

Melissa S.
Melissa S.
Numerade Educator
00:46

Problem 100

Solve each equation. Then check the result.
$$
\frac{x}{-7}=12
$$

Melissa S.
Melissa S.
Numerade Educator
01:41

Problem 101

Solve each equation. Then check the result.
$$
-\frac{15}{16} a=-\frac{5}{4}
$$

Melissa S.
Melissa S.
Numerade Educator
01:42

Problem 102

Solve each equation. Then check the result.
$$
-\frac{20}{27} b=-\frac{4}{9}
$$

Melissa S.
Melissa S.
Numerade Educator
00:42

Problem 103

Solve each equation. Then check the result.
$$
-15 x=-60
$$

Melissa S.
Melissa S.
Numerade Educator
00:44

Problem 104

Solve each equation. Then check the result.
$$
-14 x=-84
$$

Melissa S.
Melissa S.
Numerade Educator
02:27

Problem 105

LOOK Alikes...
a. $d+\frac{1}{10}=\frac{3}{4}$
b. $d-\frac{1}{10}=\frac{3}{4}$
c. $\frac{1}{10} d=\frac{3}{4}$
d. $10 d=\frac{3}{4}$

Melissa S.
Melissa S.
Numerade Educator
01:44

Problem 106

LOOK Alikes...
a. $x+4.2=-18.9$
b. $x-4.2=-18.9$
c. $4.2 x=-18.9$
d. $\frac{x}{4.2}=-18.9$

Melissa S.
Melissa S.
Numerade Educator
00:29

Problem 107

Synthesizers. To find the unknown angle measure, which is represented by $x,$ solve the equation $x+115=180$
(IMAGE CANNOT COPY)

Melissa S.
Melissa S.
Numerade Educator
00:32

Problem 108

LOOK Alikes...
Stop Signs. To find the degree measure of one angle of the stop sign, which is represented by $x,$ solve the equation $8 x=1,080$
(IMAGE CANNOT COPY)

Melissa S.
Melissa S.
Numerade Educator
00:48

Problem 109

Sharing the Winning Ticket. When a Florida Lotto Jackpot was won by a group of 16 nurses employed at a Southwest Florida Medical Center, each received $\$ 375,000 .$ To find the amount of the jackpot, which is represented by $x,$ solve the equation $\frac{x}{16}=375,000$

Melissa S.
Melissa S.
Numerade Educator
01:01

Problem 110

Social Networks. In 2009 , the annual revenue generated per employee at Twitter was $\$ 142,857 .$ This is $\$ 777,143$ less than the annual revenue generated per employee at Facebook. To find the annual revenue generated per employee at Facebook, which is represented by $x,$ solve the equation $x-777,143=142,857 .$ (Source: businessinsider.com)

Melissa S.
Melissa S.
Numerade Educator
00:09

Problem 111

What does it mean to solve an equation?

Melissa S.
Melissa S.
Numerade Educator
00:18

Problem 112

Explain the error in the following work.
Solve: $\quad-6.4 x=1.1$
$-6.4 x+6.4=1.1+6.4$
$x=7.5$

Melissa S.
Melissa S.
Numerade Educator
00:26

Problem 113

Explain the error in the following work.
$$
\begin{aligned}
\text { Solve: } & x+2=40 \\
& x+2>2=40
\end{aligned}
$$
$x=40$

Melissa S.
Melissa S.
Numerade Educator
00:14

Problem 114

After solving an equation, how do we check the result?

Melissa S.
Melissa S.
Numerade Educator
00:25

Problem 115

Evaluate $-9-3 x$ for $x=-3$

Melissa S.
Melissa S.
Numerade Educator
00:28

Problem 116

$$
\text { Evaluate: }-5^{2}+(-5)^{2}
$$

Melissa S.
Melissa S.
Numerade Educator
00:07

Problem 117

Translate to symbols: Subtract $x$ from 45

Melissa S.
Melissa S.
Numerade Educator
00:58

Problem 118

$$
\text { Evaluate: } \frac{2^{3}+3(5-3)}{15-4 \cdot 2}
$$

Melissa S.
Melissa S.
Numerade Educator
00:50

Problem 119

If $a+81=49,$ what is $a-81 ?$

Melissa S.
Melissa S.
Numerade Educator
01:08

Problem 120

Find two solutions of $\frac{1}{4}|x+1|=25$

Melissa S.
Melissa S.
Numerade Educator

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