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Beginning And Intermediate Algebra

Julie Miller, Nancy Hyde, Molly O'Neill

Chapter 1

The Set of Real Numbers - all with Video Answers

Educators


Section 1

Sets of Numbers and the Real Number Line

01:07

Problem 1

. In this text, we will provide skills for you to enhance your learning experience. In the first four chapters, each set of Practice Exercises will begin with an activity that focuses on one of the following areas: learning about your course, using your text, taking notes, doing homework, and taking an exam. In subsequent chapters, we will insert skills pertaining to the specific material in the chapter. In Chapter 6 we will give tips on studying for the final exam.

Each activity requires only a few minutes and will help you to pass this class and become a better math student. Many of these skills can be carried over to other disciplines and help you to become a model college student. To begin, fill in the following information:
a. Instructor's name
b. Days of the week that the class meets
c. The room number in which the class meets
d. Is there a lab requirement for this course? If so, how often and what is the location of the lab?
e. Instructor's office number
f. Instructor's telephone number
g. Instructor's e-mail address
h. Instructor's office hours

Dominador Tan
Dominador Tan
Numerade Educator
03:09

Problem 2

Define the key terms:
a. real numbers
b. natural numbers
c. whole numbers
d. integers
e. rational numbers
f. irrational numbers
g. inequality
h. opposite
i. absolute value
j. real number line

AL
Andrew Lebedinsky
Numerade Educator
03:01

Problem 3

Plot the numbers on a real number line: $\left\{1,-2,-\pi, 0,-\frac{5}{2}, 5.1\right\}$

Nicole Rowley
Nicole Rowley
Numerade Educator
02:47

Problem 4

Plot the numbers on a real number line: $\left\{3,-4, \frac{1}{3},-1.7,-\frac{4}{5}, 1.75\right\}$

Nicole Rowley
Nicole Rowley
Numerade Educator
01:16

Problem 5

For Exercises 5-20, Describe each number as (a) a terminating decimal, (b) a repeating decimal, or (c) a nonterminating, nonrepeating decimal.
0.29

Debasish Das
Debasish Das
Numerade Educator
01:12

Problem 6

Describe each number as (a) a terminating decimal, (b) a repeating decimal, or (c) a nonterminating, nonrepeating decimal.
3.8

Debasish Das
Debasish Das
Numerade Educator
01:38

Problem 7

Describe each number as (a) a terminating decimal, (b) a repeating decimal, or (c) a nonterminating, nonrepeating decimal.
$\frac{1}{9}$

Debasish Das
Debasish Das
Numerade Educator
01:37

Problem 8

Describe each number as (a) a terminating decimal, (b) a repeating decimal, or (c) a nonterminating, nonrepeating decimal.
$\frac{1}{3}$

Debasish Das
Debasish Das
Numerade Educator
01:34

Problem 9

Describe each number as (a) a terminating decimal, (b) a repeating decimal, or (c) a nonterminating, nonrepeating decimal.
$\frac{1}{8}$

Debasish Das
Debasish Das
Numerade Educator
01:27

Problem 10

Describe each number as (a) a terminating decimal, (b) a repeating decimal, or (c) a nonterminating, nonrepeating decimal.
$\frac{1}{5}$

Debasish Das
Debasish Das
Numerade Educator
02:13

Problem 11

Describe each number as (a) a terminating decimal, (b) a repeating decimal, or (c) a nonterminating, nonrepeating decimal.
$2 \pi$

Debasish Das
Debasish Das
Numerade Educator
01:48

Problem 12

Describe each number as (a) a terminating decimal, (b) a repeating decimal, or (c) a nonterminating, nonrepeating decimal.
$3 \pi$

Debasish Das
Debasish Das
Numerade Educator
01:38

Problem 13

Describe each number as (a) a terminating decimal, (b) a repeating decimal, or (c) a nonterminating, nonrepeating decimal.
-0.125

Debasish Das
Debasish Das
Numerade Educator
01:48

Problem 14

Describe each number as (a) a terminating decimal, (b) a repeating decimal, or (c) a nonterminating, nonrepeating decimal.
-3.24

Debasish Das
Debasish Das
Numerade Educator
01:43

Problem 15

Describe each number as (a) a terminating decimal, (b) a repeating decimal, or (c) a nonterminating, nonrepeating decimal.
-3

Debasish Das
Debasish Das
Numerade Educator
01:42

Problem 16

Describe each number as (a) a terminating decimal, (b) a repeating decimal, or (c) a nonterminating, nonrepeating decimal.
-6

Debasish Das
Debasish Das
Numerade Educator
01:40

Problem 17

Describe each number as (a) a terminating decimal, (b) a repeating decimal, or (c) a nonterminating, nonrepeating decimal.
$0 . \overline{2}$

Debasish Das
Debasish Das
Numerade Educator
01:53

Problem 18

Describe each number as (a) a terminating decimal, (b) a repeating decimal, or (c) a nonterminating, nonrepeating decimal.
$0 . \overline{6}$

Debasish Das
Debasish Das
Numerade Educator
01:51

Problem 19

Describe each number as (a) a terminating decimal, (b) a repeating decimal, or (c) a nonterminating, nonrepeating decimal.
$\sqrt{6}$

Debasish Das
Debasish Das
Numerade Educator
01:53

Problem 20

Describe each number as (a) a terminating decimal, (b) a repeating decimal, or (c) a nonterminating, nonrepeating decimal.
$\sqrt{10}$

Debasish Das
Debasish Das
Numerade Educator
00:13

Problem 21

List all of the numbers from Exercises 5-20 that are rational numbers.

Matt Gibson
Matt Gibson
Numerade Educator
00:58

Problem 22

List all of the numbers from Exercises 5-20 that are irrational numbers.

Ben Thatcher
Ben Thatcher
Numerade Educator
01:20

Problem 23

List three numbers that are real numbers but not rational numbers.

K Joseph
K Joseph
Numerade Educator
01:44

Problem 24

List three numbers that are real numbers but not irrational numbers.

K Joseph
K Joseph
Numerade Educator
01:55

Problem 25

List three numbers that are integers but not natural numbers

K Joseph
K Joseph
Numerade Educator
01:55

Problem 26

List three numbers that are integers but not whole numbers

K Joseph
K Joseph
Numerade Educator
01:55

Problem 27

List three numbers that are rational numbers but not integers.

K Joseph
K Joseph
Numerade Educator
01:55

Problem 28

For Exercises 28-33, Let $A=\left\{-\frac{1}{2}, \sqrt{11},-4,0, \overline{6}, 0, \sqrt{7}, 1\right\}$
Are all of the numbers in set $A$ real numbers?

K Joseph
K Joseph
Numerade Educator
01:44

Problem 29

Let $A=\left\{-\frac{1}{2}, \sqrt{11},-4,0, \overline{6}, 0, \sqrt{7}, 1\right\}$
List all of the rational numbers in set $A$.

K Joseph
K Joseph
Numerade Educator
01:23

Problem 30

Let $A=\left\{-\frac{1}{2}, \sqrt{11},-4,0, \overline{6}, 0, \sqrt{7}, 1\right\}$
List all of the whole numbers in set $A$.

K Joseph
K Joseph
Numerade Educator
01:36

Problem 31

Let $A=\left\{-\frac{1}{2}, \sqrt{11},-4,0, \overline{6}, 0, \sqrt{7}, 1\right\}$
List all of the natural numbers in set $A$.

K Joseph
K Joseph
Numerade Educator
01:37

Problem 32

Let $A=\left\{-\frac{1}{2}, \sqrt{11},-4,0, \overline{6}, 0, \sqrt{7}, 1\right\}$
List all of the irrational numbers in set $A$.

K Joseph
K Joseph
Numerade Educator
01:38

Problem 33

Let $A=\left\{-\frac{1}{2}, \sqrt{11},-4,0, \overline{6}, 0, \sqrt{7}, 1\right\}$
List all of the integers in set $A$.

K Joseph
K Joseph
Numerade Educator
01:38

Problem 34

Plot the real numbers of set $A$ on a number line. (Hint: $\sqrt{11} \approx 3.3$ and $\sqrt{7} \approx 2.6$ )

AL
Andrew Lebedinsky
Numerade Educator
01:33

Problem 35

The LPGA Samsung World Championship of women's golf scores for selected players are given in the table. Compare the scores and fill in the blanks with the appropriate inequality sign: $<$ or $>$.
a. Kane's score $\_\_\_\_$ Pak's score.
b. Sorenstam's score $\_\_\_\_$ Davies' score.
c. Pak's score $\_\_\_\_$ McCurdy's score.
d. Kane's score $\_\_\_\_$ Davies' score.

K Joseph
K Joseph
Numerade Educator
01:58

Problem 36

The elevations of selected cities in the United States are shown in the figure. Compare the elevations and fill in the blanks with the appropriate inequality sign: $<$ or $>$. (A negative number indicates that the city is below sea level.)
a. Elevation of Tucson $\_\_\_\_$ elevation of Cincinnati.
b. Elevation of New Orleans $\_\_\_\_$ elevation of Chicago.
c. Elevation of New Orleans $\_\_\_\_$ elevation of Houston.
d. Elevation of Chicago $\_\_\_\_$ elevation of Cincinnati.

K Joseph
K Joseph
Numerade Educator
01:17

Problem 37

For Exercises 37-44, Find the opposite of each number.
18

K Joseph
K Joseph
Numerade Educator
00:07

Problem 38

Find the opposite of each number.
2

Amy Jiang
Amy Jiang
Numerade Educator
00:18

Problem 39

Find the opposite of each number.
-6.1

Cory Kuzinski
Cory Kuzinski
Numerade Educator
00:25

Problem 40

Find the opposite of each number.
-2.5

Khanh Ha
Khanh Ha
Numerade Educator
01:24

Problem 41

Find the opposite of each number.
$-\frac{5}{8}$

K Joseph
K Joseph
Numerade Educator
01:15

Problem 42

Find the opposite of each number.
$-\frac{1}{3}$

K Joseph
K Joseph
Numerade Educator
01:44

Problem 43

Find the opposite of each number.
$\frac{7}{3}$

K Joseph
K Joseph
Numerade Educator
00:31

Problem 44

Find the opposite of each number.
$\frac{1}{9}$

Khanh Ha
Khanh Ha
Numerade Educator
01:17

Problem 45

he opposite of $a$ is denoted as $-a$. For Exercises 45-50, simplify.
$-(-3)$

K Joseph
K Joseph
Numerade Educator
01:09

Problem 46

The opposite of $a$ is denoted as $-a$. For Exercises 45-50, simplify.
$-(-5.1)$

K Joseph
K Joseph
Numerade Educator
01:20

Problem 47

The opposite of $a$ is denoted as $-a$. For Exercises 45-50, simplify.
$-\left(\frac{7}{3}\right)$

K Joseph
K Joseph
Numerade Educator
01:20

Problem 48

The opposite of $a$ is denoted as $-a$. For Exercises 45-50, simplify.
. $-(-7)$

K Joseph
K Joseph
Numerade Educator
01:35

Problem 49

The opposite of $a$ is denoted as $-a$. For Exercises 45-50, simplify.
$-(-8)$

K Joseph
K Joseph
Numerade Educator
01:19

Problem 50

The opposite of $a$ is denoted as $-a$. For Exercises 45-50, simplify.
$-(36)$

K Joseph
K Joseph
Numerade Educator
01:31

Problem 51

For Exercises 51-58, Find the absolute value as indicated.
$|-2|$

Suman Saurav Thakur
Suman Saurav Thakur
Numerade Educator
00:16

Problem 52

Find the absolute value as indicated.
$|-7|$

John Irizar
John Irizar
Numerade Educator
00:11

Problem 53

Find the absolute value as indicated.
$|-1.5|$

Ramzi Deek
Ramzi Deek
Numerade Educator
01:27

Problem 54

Find the absolute value as indicated.
$|-3.7|$

K Joseph
K Joseph
Numerade Educator
00:11

Problem 55

Find the absolute value as indicated.
$-|-1.5|$

Ramzi Deek
Ramzi Deek
Numerade Educator
01:27

Problem 56

Find the absolute value as indicated.
$-|-3.7|$

K Joseph
K Joseph
Numerade Educator
02:30

Problem 57

Find the absolute value as indicated.
$\left|\frac{3}{2}\right|$

Anas Venkitta
Anas Venkitta
Numerade Educator
00:12

Problem 58

Find the absolute value as indicated.
$\left|\frac{7}{4}\right|$

AG
Ankit Gupta
Numerade Educator
01:19

Problem 59

For Exercises 59-60, answer true or false. If a statement is false, explain why.
If $n$ is positive, then $|n|$ is negative.

K Joseph
K Joseph
Numerade Educator
01:19

Problem 60

For Exercises 59-60, answer true or false. If a statement is false, explain why.
If $m$ is negative, then $|m|$ is negative.

K Joseph
K Joseph
Numerade Educator
01:18

Problem 61

For Exercises 61-84, Determine if the statements are true or false. Use the real number line to justify the answer.
$5>2$

K Joseph
K Joseph
Numerade Educator
01:24

Problem 62

Determine if the statements are true or false. Use the real number line to justify the answer.
$8<10$

K Joseph
K Joseph
Numerade Educator
01:36

Problem 63

Determine if the statements are true or false. Use the real number line to justify the answer.
. $6<6$

K Joseph
K Joseph
Numerade Educator
01:36

Problem 64

Determine if the statements are true or false. Use the real number line to justify the answer.
. $19>19$

K Joseph
K Joseph
Numerade Educator
01:23

Problem 65

Determine if the statements are true or false. Use the real number line to justify the answer.
. $-7 \geq-7$

K Joseph
K Joseph
Numerade Educator
01:23

Problem 66

Determine if the statements are true or false. Use the real number line to justify the answer.
$-1 \leq-1$

K Joseph
K Joseph
Numerade Educator
01:36

Problem 67

Determine if the statements are true or false. Use the real number line to justify the answer.
$\frac{3}{2} \leq \frac{1}{6}$

K Joseph
K Joseph
Numerade Educator
01:36

Problem 68

Determine if the statements are true or false. Use the real number line to justify the answer.
$-\frac{1}{4} \geq-\frac{7}{8}$

K Joseph
K Joseph
Numerade Educator
01:36

Problem 69

Determine if the statements are true or false. Use the real number line to justify the answer.
$-5>-2$

K Joseph
K Joseph
Numerade Educator
01:36

Problem 70

Determine if the statements are true or false. Use the real number line to justify the answer.
$6<-10$

K Joseph
K Joseph
Numerade Educator
01:36

Problem 71

Determine if the statements are true or false. Use the real number line to justify the answer.
$8 \neq 8$

K Joseph
K Joseph
Numerade Educator
01:36

Problem 72

Determine if the statements are true or false. Use the real number line to justify the answer.
. $10 \neq 10$

K Joseph
K Joseph
Numerade Educator
01:23

Problem 73

Determine if the statements are true or false. Use the real number line to justify the answer.
$|-2| \geq|-1|$

K Joseph
K Joseph
Numerade Educator
01:36

Problem 74

Determine if the statements are true or false. Use the real number line to justify the answer.
$|3| \leq|-1|$

K Joseph
K Joseph
Numerade Educator
01:23

Problem 75

Determine if the statements are true or false. Use the real number line to justify the answer.
. $\left|-\frac{1}{9}\right|=\left|\frac{1}{9}\right|$

K Joseph
K Joseph
Numerade Educator
01:23

Problem 76

Determine if the statements are true or false. Use the real number line to justify the answer.
$\left|-\frac{1}{3}\right|=\left|\frac{1}{3}\right|$

K Joseph
K Joseph
Numerade Educator
01:36

Problem 77

Determine if the statements are true or false. Use the real number line to justify the answer.
$|7| \neq|-7|$

K Joseph
K Joseph
Numerade Educator
01:36

Problem 78

Determine if the statements are true or false. Use the real number line to justify the answer.
. $|-13| \neq|13|$

K Joseph
K Joseph
Numerade Educator
01:23

Problem 79

Determine if the statements are true or false. Use the real number line to justify the answer.
$-1<|-1|$

K Joseph
K Joseph
Numerade Educator
01:23

Problem 80

Determine if the statements are true or false. Use the real number line to justify the answer.
$-6<|-6|$

K Joseph
K Joseph
Numerade Educator
01:23

Problem 81

Determine if the statements are true or false. Use the real number line to justify the answer.
$|-8| \geq|8|$

K Joseph
K Joseph
Numerade Educator
01:23

Problem 82

Determine if the statements are true or false. Use the real number line to justify the answer.
$|-11| \geq|11|$

K Joseph
K Joseph
Numerade Educator
01:23

Problem 83

Determine if the statements are true or false. Use the real number line to justify the answer.
$|-2| \leq \mid 2$

K Joseph
K Joseph
Numerade Educator
01:23

Problem 84

Determine if the statements are true or false. Use the real number line to justify the answer.
$|-21| \leq|21|$

K Joseph
K Joseph
Numerade Educator
01:57

Problem 85

For what numbers, $a$, is $-a$ positive?

Debasish Das
Debasish Das
Numerade Educator
01:17

Problem 86

For what numbers, $a$, is $|a|=a$ ?

Debasish Das
Debasish Das
Numerade Educator