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  • Introduction to Algebra

Prealgebra

Charles P. McKeague

Chapter 2

Introduction to Algebra - all with Video Answers

Educators


Section 1

Positive and Negative Numbers

Problem 1

Write each of the following in words.
$$4<7$$

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Problem 2

Write each of the following in words.
$$0<10$$

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Problem 3

Write each of the following in words.
$$5>-2$$

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Problem 4

Write each of the following in words.
$$8>-8$$

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Problem 5

Write each of the following in words.
$$-10<-3$$

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Problem 6

Write each of the following in words.
$$-20<-5$$

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Problem 7

Write each of the following in words.
$$0>-4$$

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Problem 8

Write each of the following in words.
$$0>-100$$

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Problem 9

Write each of the following in symbols.
30 is greater than $-30$

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Problem 10

Write each of the following in symbols.
$-30$ is less than 30

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Problem 11

Write each of the following in symbols.
10 is less than $0 .$

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Problem 12

Write each of the following in symbols.
0 is greater than $-10$

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Problem 13

Write each of the following in symbols.
$-3$ is greater than $-15$

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Problem 14

Write each of the following in symbols.
$-15$ is less than $-3$

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Problem 15

Place either < or $>$ between each of the following pairs of numbers so that the resulting statement is true. 3 $\quad$ 7

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Problem 16

Place either < or $>$ between each of the following pairs of numbers so that the resulting statement is true. $$17 \quad 0$$

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Problem 17

Place either < or $>$ between each of the following pairs of numbers so that the resulting statement is true. $$7 \quad -5$$

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Problem 18

Place either < or $>$ between each of the following pairs of numbers so that the resulting statement is true. $$2 \quad -13$$

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Problem 19

Place either < or $>$ between each of the following pairs of numbers so that the resulting statement is true. $$-6 \quad 0$$

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Problem 20

Place either < or $>$ between each of the following pairs of numbers so that the resulting statement is true. $$-14 \quad 0$$

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Problem 21

Place either < or $>$ between each of the following pairs of numbers so that the resulting statement is true. $$-12 \quad -2$$

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Problem 22

Place either < or $>$ between each of the following pairs of numbers so that the resulting statement is true. $$-20 \quad -1$$

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Problem 23

Place either < or $>$ between each of the following pairs of numbers so that the resulting statement is true. $$-\frac{1}{2}\quad-\frac{3}{4}$$

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Problem 24

Place either < or $>$ between each of the following pairs of numbers so that the resulting statement is true. $$-\frac{6}{7} \quad \frac{5}{6}$$

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Problem 25

Place either < or $>$ between each of the following pairs of numbers so that the resulting statement is true. $$-0.75 \quad 0.25$$

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Problem 26

Place either < or $>$ between each of the following pairs of numbers so that the resulting statement is true. $$-1 \quad-3.5$$

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Problem 27

Place either < or $>$ between each of the following pairs of numbers so that the resulting statement is true. $$-0.1 \quad-0.01$$

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Problem 28

Place either < or $>$ between each of the following pairs of numbers so that the resulting statement is true. $$-0.04\quad-0.4$$

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Problem 29

Place either < or $>$ between each of the following pairs of numbers so that the resulting statement is true. $$-3 \quad|6|$$

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Problem 30

Place either < or $>$ between each of the following pairs of numbers so that the resulting statement is true. $$|8| \quad -2$$

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Problem 31

Place either < or $>$ between each of the following pairs of numbers so that the resulting statement is true. $$15 \quad|-4|$$

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Problem 32

Place either < or $>$ between each of the following pairs of numbers so that the resulting statement is true. $$20 \quad|-6|$$

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Problem 33

Place either < or $>$ between each of the following pairs of numbers so that the resulting statement is true. $$|-2| \quad|-7|$$

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Problem 34

Place either < or $>$ between each of the following pairs of numbers so that the resulting statement is true. $$|-3| \quad|-1|$$

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Problem 35

Find each of the following absolute values.
$$|2|$$

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Problem 36

Find each of the following absolute values.
$$|7|$$

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Problem 37

Find each of the following absolute values.
$$|100|$$

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Problem 38

Find each of the following absolute values.
$$|10,000|$$

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Problem 39

Find each of the following absolute values.
$$|-8|$$

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Problem 40

Find each of the following absolute values.
$$|-9|$$

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Problem 41

Find each of the following absolute values.
$$|-231|$$

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Problem 42

Find each of the following absolute values.
$$|-457|$$

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Problem 43

Find each of the following absolute values.
$$\left|-\frac{3}{4}\right|$$

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Problem 44

Find each of the following absolute values.
$$\left|-\frac{1}{10}\right|$$

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Problem 45

Find each of the following absolute values.
$$|-200|$$

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Problem 46

Find each of the following absolute values.
$$|-350|$$

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Problem 47

Find each of the following absolute values.
$$|8|$$

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Problem 48

Find each of the following absolute values.
$$|9|$$

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Problem 49

Find each of the following absolute values.
$$|231|$$

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Problem 50

Find each of the following absolute values.
$$|457|$$

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Problem 51

Give the opposite of each of the following numbers.
$$3$$

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Problem 52

Give the opposite of each of the following numbers.
$$-5$$

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Problem 53

Give the opposite of each of the following numbers.
$$-2$$

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Problem 54

Give the opposite of each of the following numbers.
$$15$$

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Problem 55

Give the opposite of each of the following numbers.
$$75$$

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Problem 56

Give the opposite of each of the following numbers.
$$-32$$

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Problem 57

Give the opposite of each of the following numbers.
$$0$$

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Problem 58

Give the opposite of each of the following numbers.
$$1$$

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Problem 59

Give the opposite of each of the following numbers.
$$-121$$

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Problem 60

Give the opposite of each of the following numbers.
$$-200$$

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Problem 61

Give the opposite of each of the following numbers.
$$555$$

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Problem 62

Give the opposite of each of the following numbers.
$$125$$

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Problem 63

Simplify each of the following.
$$-(-2)$$

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Problem 64

Simplify each of the following.
$$-(-5)$$

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Problem 65

Simplify each of the following.
$$-(-8)$$

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Problem 66

Simplify each of the following.
$$-(-3)$$

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Problem 67

Simplify each of the following.
$$-|-2|$$

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Problem 68

Simplify each of the following.
$$-|-5|$$

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Problem 69

Simplify each of the following.
$$-|-8|$$

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Problem 70

Simplify each of the following.
$$-|-3|$$

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Problem 71

What number is its own opposite?

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Problem 72

Is $|a|=a$ always a true statement?

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Problem 73

If $n$ is a negative number, is $-n$ positive or negative?

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Problem 74

If $n$ is a positive number, is $-n$ positive or negative?

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Problem 75

Without pencil and paper or a calculator.
Is $-60$ closer to 0 or $-100 ?$

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Problem 76

Without pencil and paper or a calculator.
Is $-20$ closer to 0 or $-30 ?$

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Problem 77

Without pencil and paper or a calculator.
Is $-10$ closer to $-20$ or $20 ?$

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Problem 78

Without pencil and paper or a calculator.
Is $-20$ closer to $-40$ or $10 ?$

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Problem 79

Without pencil and paper or a calculator.
Is $-362$ closer to $-360$ or $-370 ?$

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Problem 80

Without pencil and paper or a calculator.
Is $-368$ closer to $-360$ or $-370 ?$

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Problem 81

The London Eye has a height of 450 feet. Describe the location of someone standing on the ground in relation to someone at the top of the London Eye.

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Problem 82

The Eiffel Tower has several levels visitors can walk around on. The first is 57 meters above the ground, the second is 115 meters high, and the third level is 276 meters high. What is the location of someone standing on the first level in relation to someone standing on the third level?

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Problem 83

The Bright Angel trail at Grand Canyon National Park ends at Indian Garden, $3,060$ feet below the trailhead. Write this as a negative number with respect to the trailhead.

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Problem 84

The South Kaibab Trail at Grand Canyon National Park ends at Cedar Ridge, $1,140$ feet below the trailhead. Write this as a negative number with respect to the trailhead.

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Problem 85

Depreciation refers to the decline in a car's market value during the time you own the car. According to sources such as Kelley Blue Book and Edmunds.com, not all cars depreciate at the same rate. Suppose you pay 25,000 dollars for a new car which has a high rate of depreciation. Your car loses about 5,000 dollars in value per year. Represent this loss in value as a negative number. A car with a low rate of depreciation loses about 2,750 dollars in value each year. Represent this loss as a negative number.

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Problem 86

In June, 2007 the U.S. Census Bureau released population estimates for the twenty-five cities with the largest population loss between July $1,2005$ and July $1,2006 .$ New Orleans had the largest population loss. The city's population fell by $228,782$ people. Detroit, Michigan experienced a population loss of $12,344$ people during the same time period. Represent the loss of population for New Orleans and for Detroit as a negative number.

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Problem 87

Yamina is flying from Phoenix to San Francisco on a Boeing 737 jet. When the plane reaches an altitude of $33,000$ feet, the temperature outside the plane is 61 degrees below zero Fahrenheit. Represent this temperature with a negative number. If the temperature outside the plane gets warmer by 10 degrees, what will the new temperature be?

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Problem 88

At 11: 00 in the morning in Superior, Wisconsin, Jim notices the temperature is 15 degrees below zero Fahrenheit. Write this temperature as a negative number. At noon it has warmed up by 8 degrees. What is the temperature at noon?

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Problem 89

At 10: 00 in the morning in White Bear Lake, Minnesota, Zach notices the temperature is 5 degrees below zero Fahrenheit. Write this temperature as a negative number. By noon the temperature has dropped another 10 degrees. What is the temperature at noon?

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Problem 90

Steve is snorkeling in the ocean near his home in Maui. At one point he is 6 feet below the surface. Represent this situation with a negative number. If he descends another 6 feet, what negative number will represent his new position?

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Problem 91

New Orleans, Louisiana, is 1 time zone west of New York City. Represent this time zone as a negative number, as discussed in the introduction to this chapter.

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Problem 92

Seattle, Washington, is 2 time zones west of New Orleans, Louisiana. Represent this time zone as a negative number, as discussed in the introduction to this chapter.

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Problem 93

Find the wind chill temperature if the thermometer reads $25^{\circ} \mathrm{F}$ and the wind is blowing at 25 miles per hour.

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Problem 94

Find the wind chill temperature if the thermometer reads $10^{\circ} \mathrm{F}$ and the wind is blowing at 25 miles per hour.

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Problem 95

Which will feel colder: a day with an air temperature of $10^{\circ} \mathrm{F}$ and a 25 -mph wind, or a day with an air temperature of $-5^{\circ} \mathrm{F}$ and a $10-\mathrm{mph}$ wind?

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Problem 96

Which will feel colder: a day with an air temperature of $15^{\circ} \mathrm{F}$ and a 20 -mph wind, or a day with an air temperature of $5^{\circ} \mathrm{F}$ and a $10-\mathrm{mph}$ wind?

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Problem 97

Figure 5 is a bar chart of the information in Table $3 .$ Use the template in Figure 6 to construct a scatter diagram of the same information. Then connect the dots in the scatter diagram to obtain a line graph of that same information. (Notice that we have used the numbers 1 through 12 to represent the months January through December.) (GRAPH CANNOT COPY).

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Problem 98

Figure 7 is a bar chart of the information in Table $4 .$ Use the template in Figure 8 to construct a scatter diagram of the same information. Then connect the dots in the scatter diagram to obtain a line graph of that same information. (Again, we have used the numbers 1 through 12 to represent the months January through December.) (GRAPH CANNOT COPY).

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Problem 99

Add or subtract.
$$10+15$$

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Problem 100

Add or subtract.
$$12+15$$

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Problem 101

Add or subtract.
$$15-10$$

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Problem 102

Add or subtract.
$$15-12$$

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Problem 103

Add or subtract.
$$10-5-3+4$$

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Problem 104

Add or subtract.
$$12-3-7+5$$

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Problem 105

Add or subtract.
$$[3+10]+[8-2]$$

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Problem 106

Add or subtract.
$$[2+12]+[7-5]$$

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Problem 107

Add or subtract.
$$276+32+4,005$$

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Problem 108

Add or subtract.
$$17+3+152+1,200$$

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Problem 109

Add or subtract.
$$635-579$$

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Problem 110

Add or subtract.
$$2,987-1,130$$

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