Contemporary Precalculus

Thomas W. Hungerford, Douglas J. Shaw

Chapter 1

Basics - all with Video Answers

Educators

Section 1

The Real Number System

Problem 1

Draw a number line and mark the location of each of these numbers: $0,-7,8 / 3,10,-1,-4.75,1 / 2,-5,$ and 2.25

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Problem 2

Use your calculator to determine which of the following rational numbers is the best approximation of the irrational number $\pi$
$$\frac{22}{7}, \quad \frac{355}{113}, \quad \frac{103,993}{33,102}, \quad \frac{2,508,429,787}{798,458,000}$$
If your calculator says that one of these numbers equals $\pi$ it's lying. All you can conclude is that the number agrees with $\pi$ for as many decimal places as your calculator can handle (usually $12-14$ ).

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Problem 3

$b, c,$ and $d$ are real numbers such that $b<0$ $c>0,$ and $d<0 .$ Determine whether the given number is positive or negative.
$$-b$$

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Problem 4

$b, c,$ and $d$ are real numbers such that $b<0$ $c>0,$ and $d<0 .$ Determine whether the given number is positive or negative.
$$-\boldsymbol{c}$$

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Problem 5

$b, c,$ and $d$ are real numbers such that $b<0$ $c>0,$ and $d<0 .$ Determine whether the given number is positive or negative.
$$b c d$$

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Problem 6

$b, c,$ and $d$ are real numbers such that $b<0$ $c>0,$ and $d<0 .$ Determine whether the given number is positive or negative.
$$b-c$$

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Problem 7

$b, c,$ and $d$ are real numbers such that $b<0$ $c>0,$ and $d<0 .$ Determine whether the given number is positive or negative.
$$b c-b d$$

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Problem 8

$b, c,$ and $d$ are real numbers such that $b<0$ $c>0,$ and $d<0 .$ Determine whether the given number is positive or negative.
$$b^{2} c-c^{2} d$$

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Problem 9

Use a calculator and list the given numbers in order from smallest to largest.
$$\frac{189}{37}, \frac{4587}{691}, \quad \sqrt{47}, \quad 6.735, \quad \sqrt{27}, \quad \frac{2040}{523}$$

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Problem 10

Use a calculator and list the given numbers in order from smallest to largest.
$$\frac{385}{177}, \quad \sqrt{10}, \quad \frac{187}{63}, \quad \pi, \quad \sqrt{\sqrt{85}}, \quad 2.9884$$

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Problem 11

Express the given statement in symbols.
-4 is greater than -8

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Problem 12

Express the given statement in symbols.
-17 is less than 6

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Problem 13

Express the given statement in symbols.
$\pi$ is less than 100

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Problem 14

Express the given statement in symbols.
$x$ is nonnegative.

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Problem 15

Express the given statement in symbols.
$z$ is greater than or equal to -4

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Problem 16

Express the given statement in symbols.
$t$ is negative.

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Problem 17

Express the given statement in symbols.
$d$ is not greater than 7

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Problem 18

Express the given statement in symbols.
$c$ is at most 3

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Problem 19

Express the given statement in symbols.
$z$ is at least -17

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Problem 20

Fill the blank with $<,=,$ or $>$ so that the resulting statement is true.
-6 ______ -2

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Problem 21

Fill the blank with $<,=,$ or $>$ so that the resulting statement is true.
5 ______ -3

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Problem 22

Fill the blank with $<,=,$ or $>$ so that the resulting statement is true.
$3 / 4$ ______ .75

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Problem 23

Fill the blank with $<,=,$ or $>$ so that the resulting statement is true.
3.1416 ______ $\pi$

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Problem 24

Fill the blank with $<,=,$ or $>$ so that the resulting statement is true.
$1 / 3$ ______ .33

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Problem 25

The consumer price index for urban consumers (CPI-U) measures the cost of consumer goods and services such as food, housing, transportation, medical costs, etc. The table shows the yearly percentage increase in the CPI-U over a decade.$*$
$$\begin{array}{|c|c|}
\hline \text { Year } & \text { Percentage change } \\
\hline 1996 & 3.0 \\
\hline 1997 & 2.3 \\
\hline 1998 & 1.6 \\
\hline 1999 & 2.2 \\
\hline 2000 & 3.4 \\
\hline 2001 & 2.8 \\
\hline 2002 & 1.6 \\
\hline 2003 & 2.3 \\
\hline 2004 & 2.7 \\
\hline 2005 & 2.5 \\
\hline
\end{array}$$
Let $p$ denote the yearly percentage increase in the CPI-U. Find the number of years in this period which satisfied the given inequality.
$$p \geq 2.8$$

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Problem 26

The consumer price index for urban consumers (CPI-U) measures the cost of consumer goods and services such as food, housing, transportation, medical costs, etc. The table shows the yearly percentage increase in the CPI-U over a decade.$*$
$$\begin{array}{|c|c|}
\hline \text { Year } & \text { Percentage change } \\
\hline 1996 & 3.0 \\
\hline 1997 & 2.3 \\
\hline 1998 & 1.6 \\
\hline 1999 & 2.2 \\
\hline 2000 & 3.4 \\
\hline 2001 & 2.8 \\
\hline 2002 & 1.6 \\
\hline 2003 & 2.3 \\
\hline 2004 & 2.7 \\
\hline 2005 & 2.5 \\
\hline
\end{array}$$
Let $p$ denote the yearly percentage increase in the CPI-U. Find the number of years in this period which satisfied the given inequality.
$$p<2.6$$

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Problem 27

The consumer price index for urban consumers (CPI-U) measures the cost of consumer goods and services such as food, housing, transportation, medical costs, etc. The table shows the yearly percentage increase in the CPI-U over a decade.$*$
$$\begin{array}{|c|c|}
\hline \text { Year } & \text { Percentage change } \\
\hline 1996 & 3.0 \\
\hline 1997 & 2.3 \\
\hline 1998 & 1.6 \\
\hline 1999 & 2.2 \\
\hline 2000 & 3.4 \\
\hline 2001 & 2.8 \\
\hline 2002 & 1.6 \\
\hline 2003 & 2.3 \\
\hline 2004 & 2.7 \\
\hline 2005 & 2.5 \\
\hline
\end{array}$$
Let $p$ denote the yearly percentage increase in the CPI-U. Find the number of years in this period which satisfied the given inequality.
$$p>2.3$$

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Problem 28

The consumer price index for urban consumers (CPI-U) measures the cost of consumer goods and services such as food, housing, transportation, medical costs, etc. The table shows the yearly percentage increase in the CPI-U over a decade.$*$
$$\begin{array}{|c|c|}
\hline \text { Year } & \text { Percentage change } \\
\hline 1996 & 3.0 \\
\hline 1997 & 2.3 \\
\hline 1998 & 1.6 \\
\hline 1999 & 2.2 \\
\hline 2000 & 3.4 \\
\hline 2001 & 2.8 \\
\hline 2002 & 1.6 \\
\hline 2003 & 2.3 \\
\hline 2004 & 2.7 \\
\hline 2005 & 2.5 \\
\hline
\end{array}$$
Let $p$ denote the yearly percentage increase in the CPI-U. Find the number of years in this period which satisfied the given inequality.
$$p \leq 3.0$$

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Problem 29

The consumer price index for urban consumers (CPI-U) measures the cost of consumer goods and services such as food, housing, transportation, medical costs, etc. The table shows the yearly percentage increase in the CPI-U over a decade.$*$
$$\begin{array}{|c|c|}
\hline \text { Year } & \text { Percentage change } \\
\hline 1996 & 3.0 \\
\hline 1997 & 2.3 \\
\hline 1998 & 1.6 \\
\hline 1999 & 2.2 \\
\hline 2000 & 3.4 \\
\hline 2001 & 2.8 \\
\hline 2002 & 1.6 \\
\hline 2003 & 2.3 \\
\hline 2004 & 2.7 \\
\hline 2005 & 2.5 \\
\hline
\end{array}$$
Let $p$ denote the yearly percentage increase in the CPI-U. Find the number of years in this period which satisfied the given inequality.
$$p>3.4$$

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Problem 30

Fill the blank so as to produce two equivalent statements. For example, the arithmetic statement "a is negative" is equivalent to the geometric statement "the point a lies to the left of the point $0 . "$
Arithmetic Statement
$a \geq b$
Geometric Statement
______

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Problem 31

Fill the blank so as to produce two equivalent statements. For example, the arithmetic statement "a is negative" is equivalent to the geometric statement "the point a lies to the left of the point $0 . "$
Arithmetic Statement
______
Geometric Statement
$a$ lies $c$ units to the right of $b$

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Problem 32

Fill the blank so as to produce two equivalent statements. For example, the arithmetic statement "a is negative" is equivalent to the geometric statement "the point a lies to the left of the point $0 . "$
Arithmetic Statement
______
Geometric Statement
$a$ lies between $b$ and $c$

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Problem 33

Fill the blank so as to produce two equivalent statements. For example, the arithmetic statement "a is negative" is equivalent to the geometric statement "the point a lies to the left of the point $0 . "$
Arithmetic Statement
$a-b>0$
Geometric Statement
______

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Problem 33

Draw a picture on the number line of the given interval.
$$(0, \infty)$$

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Problem 34

Fill the blank so as to produce two equivalent statements. For example, the arithmetic statement "a is negative" is equivalent to the geometric statement "the point a lies to the left of the point $0 . "$
Arithmetic Statement
$a$ is positive
Geometric Statement
______

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Problem 35

Fill the blank so as to produce two equivalent statements. For example, the arithmetic statement "a is negative" is equivalent to the geometric statement "the point a lies to the left of the point $0 . "$
Arithmetic Statement
______
Geometric Statement
$a$ lies to the left of $b$

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Problem 36

Fill the blank so as to produce two equivalent statements. For example, the arithmetic statement "a is negative" is equivalent to the geometric statement "the point a lies to the left of the point $0 . "$
Arithmetic Statement
$a+b<c \quad(b>0)$
Geometric Statement
______

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Problem 37

Draw a picture on the number line of the given interval.
$$(0,8]$$

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Problem 39

Draw a picture on the number line of the given interval.
$$[-2,1]$$

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Problem 40

Draw a picture on the number line of the given interval.
$$(-1,1)$$

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Problem 41

Draw a picture on the number line of the given interval.
$$(-\infty, 0]$$

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Problem 42

Draw a picture on the number line of the given interval.
$$[-2,7)$$

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Problem 43

Use interval notation to denote the set of all real numbers $x$ that satisfy the given inequality.
$$5 \leq x \leq 10$$

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Problem 44

Use interval notation to denote the set of all real numbers $x$ that satisfy the given inequality.
$$-2 \leq x \leq 7$$

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Problem 45

Use interval notation to denote the set of all real numbers $x$ that satisfy the given inequality.
$$-3<x<14$$

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Problem 46

Use interval notation to denote the set of all real numbers $x$ that satisfy the given inequality.
$$7<x<77$$

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Problem 47

Use interval notation to denote the set of all real numbers $x$ that satisfy the given inequality.
$$x \geq-9$$

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Problem 48

Use interval notation to denote the set of all real numbers $x$ that satisfy the given inequality.
$$x \geq 12$$

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Problem 49

Express the given numbers (based on 2006 estimates) in scientific notation.
Population of the world: 6,506,000,000

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Problem 50

Express the given numbers (based on 2006 estimates) in scientific notation.
Population of the United States: 298,400,000

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Problem 51

Express the given numbers (based on 2006 estimates) in scientific notation.
Average distance from Earth to Pluto: 5,910,000,000,000 meters

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Problem 52

Express the given numbers (based on 2006 estimates) in scientific notation.
Radius of a hydrogen atom: .00000000001 meter

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Problem 53

Express the given numbers (based on 2006 estimates) in scientific notation.
Width of a DNA double helix: .000000002 meter

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Problem 54

Express the given number in normal decimal notation.
Speed of light in a vacuum: $2.9979 \times 10^{8}$ miles per second

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Problem 55

Express the given number in normal decimal notation.
Average distance from the earth to the sun: $1.50 \times 10^{11}$ meters

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Problem 56

Express the given number in normal decimal notation.
Electron charge: $1.602 \times 10^{-27}$ coulomb

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Problem 57

Electron charge: $1.602 \times 10^{-27}$ coulomb
Proton mass: $1.6726 \times 10^{-19}$ kilogram

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Problem 58

Express the given number in normal decimal notation.
One light-year is the distance light travels in a 365 -day year. The speed of light is about 186,282.4 miles per second.
(a) How long is 1 light-year (in miles)? Express your answer in scientific notation.
(b) Light from the North Star takes 680 years to reach the earth. How many miles is the North Star from the earth?

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Problem 59

The gross federal debt was about 8365 billion dollars in 2006 , when the U.S. population was approximately 298.4 million people.
(a) Express the debt and the population in scientific notation.
(b) At that time, what was each person's share of the federal debt?

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Problem 60

Apple reported that it had sold 28 million iPods through the end of 2005 and that 14 million iPods were sold in the first quarter of $2006 .$ If the rate in the first quarter of 2006 continues through the end of $2008,$ how many iPods will be sold? Express your answer in scientific notation.

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Problem 61

Simplify the expression without using a calculator. Your answer should not have any radicals in it.
$$\sqrt{2} \sqrt{8}$$

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Problem 62

Simplify the expression without using a calculator. Your answer should not have any radicals in it.
$$\sqrt{12} \sqrt{3}$$

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Problem 63

Simplify the expression without using a calculator. Your answer should not have any radicals in it.
$$\sqrt{\frac{3}{5}} \sqrt{\frac{12}{5}}$$

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Problem 64

Simplify the expression without using a calculator. Your answer should not have any radicals in it.
$$\sqrt{\frac{1}{2}} \sqrt{\frac{1}{6}} \sqrt{\frac{1}{12}}$$

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Problem 65

Simplify the expression without using a calculator. Your answer should not have any radicals in it.
$$\sqrt{6}+\sqrt{2}(\sqrt{2}-\sqrt{3})$$

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Problem 66

Simplify the expression without using a calculator. Your answer should not have any radicals in it.
$$\sqrt{12}(\sqrt{3}-\sqrt{27})$$

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Problem 67

Simplify the expression without using a calculator. Your answer should not have any radicals in it.
$\sqrt{u^{4}}(u \text { any real number })$ 68

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Problem 68

Simplify the expression without using a calculator. Your answer should not have any radicals in it.
$\sqrt{3 x} \sqrt{75 x^{3}}(x \geq 0)$

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Problem 69

Simplify, and write the given number without using absolute values.
$$|3-14|$$

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Problem 70

Simplify, and write the given number without using absolute values.
$$|(-2) 3|$$

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Problem 71

Simplify, and write the given number without using absolute values.
$$3-|2-5|$$

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Problem 72

Simplify, and write the given number without using absolute values.
$$-2-|-2|$$

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Problem 73

Simplify, and write the given number without using absolute values.
$$\left|(-13)^{2}\right|$$

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Problem 74

Simplify, and write the given number without using absolute values.
$$-|-5|^{2}$$

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Problem 75

Simplify, and write the given number without using absolute values.
$$|\pi-\sqrt{2}|$$

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Problem 76

Simplify, and write the given number without using absolute values.
$$|\sqrt{2}-2|$$

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Problem 77

Simplify, and write the given number without using absolute values.
$$|3-\pi|+3$$

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Problem 78

Simplify, and write the given number without using absolute values.
$$|4-\sqrt{2}|-5$$

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Problem 79

Fill the blank with $<,=$, or $>$ so that the resulting statement is true.
|-2| ______ |-5|

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Problem 80

Fill the blank with $<,=$, or $>$ so that the resulting statement is true.
5 ________ |-2|

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Problem 81

Fill the blank with $<,=$, or $>$ so that the resulting statement is true.
|3| __________-|4|

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Problem 82

Fill the blank with $<,=$, or $>$ so that the resulting statement is true.
|-3| ________ 0

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Problem 83

Fill the blank with $<,=,$ or $>$ so that the resulting statement is true.
-7= _______ |-1|

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Problem 84

Fill the blank with $<,=,$ or $>$ so that the resulting statement is true.
-|-4| _________ 0

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Problem 85

Find the distance between the given numbers.
-3 and 4

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Problem 86

Find the distance between the given numbers.
7 and 107

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Problem 87

Fill the blank with $<,=,$ or $>$ so that the resulting statement is true.
-7 and $15 / 2$

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Problem 88

Fill the blank with $<,=,$ or $>$ so that the resulting statement is true.
$-3 / 4$ and -10

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Problem 89

Fill the blank with $<,=,$ or $>$ so that the resulting statement is true.
$\pi$ and 3

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Problem 90

Find the distance between the given numbers.
$\pi$ and -3

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Problem 91

Find the distance between the given numbers.
$\sqrt{2}$ and $\sqrt{3}$

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Problem 92

Find the distance between the given numbers.
$\pi$ and $\sqrt{2}$

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Problem 93

Galileo discovered that the period of a pendulum depends only on the length of the pendulum and the acceleration of gravity. The period $T$ of a pendulum (in seconds) is
$$T=2 \pi \sqrt{\frac{l}{g}}$$
where $l$ is the length of the pendulum in feet and $g \approx$ 32.2 $\mathrm{ft} / \mathrm{sec}^{2}$ is the acceleration due to gravity. Find the period of a pendulum whose length is 4 feet.

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Problem 94

Suppose you are $k$ miles (not feet) above the ground. The radius of the earth is approximately 3960 miles. At the point where your line of sight meets the earth, it is perpendicular to the radius of the earth, as shown in the figure.
(FIGURE CANNOT COPY)
(a) Use the Pythagorean Theorem (see the Geometry Review Appendix) to show that
$$
d=\sqrt{(3960+k)^{2}-3960^{2}}
$$
(b) Show that the equation in part (a) simplifies to
$$
d=\sqrt{7920 k+k^{2}}
$$
(c) If you are $h$ feet above the ground, then you are $h / 5280$ miles high (why?). Use this fact and the equation in part (b) to obtain the formula used

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Problem 95

According to data from the Center for Science in the Public Interest, the healthy weight range for a person depends on the person's height. For example,
Height
$5 \mathrm{ft} 8 \mathrm{in}$
$6 \mathrm{ft} 0 \mathrm{in}$
Healthy Weight Range ( $\mathbf{l b}$ )
$143 \pm 21$
$163 \pm 26$

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Problem 96

At Statewide Insurance, each department's expenses are reviewed monthly. A department can fail to pass the budget variance test in a category if either (i) the absolute value of the difference between actual expenses and the budget is more than $\$ 500$ or (ii) the absolute value of the difference between the actual expenses and the budget is more than $5 \%$ of the budgeted amount. Which of the following items fail the budget variance test? Explain your answers.
$$\begin{array}{|l|c|c|}
\hline \multirow{2}{*}\text { Item } & \multirow{2}{*}\begin{array}{c}
\text { Budgeted } \\
\text { Expense (\$) }
\end{array} & \multirow{2}{*}\begin{array}{c}
\text { Actual } \\
\text { Expense (\$) }
\end{array} \\
\hline \text { Wages } & 220,750 & 221,239 \\
\hline \text { Overtime } & 10,500 & 11,018 \\
\hline \begin{array}{l}
\text { Shipping and } \\
\text { Postage }
\end{array} & \multirow{2}{*}530 & \multirow{2}{*}589 \\
\hline
\end{array}$$

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Problem 97

The wind-chill factor, shown in the table, calculates how a given temperature feels to a person's skin when the wind is taken into account. For example, the table shows that a temperature of 20 in a 40 mph wind feels like $-1 .^{\text {at }}$
(TABLE CANNOT COPY)
Find the absolute value of the difference of the two given wind-chill factors. For example, the difference between the wind-chill at 30 with a 15 mph wind and one at
-10 with a 10 mph wind is $|19-(-28)|=47^{\circ}$ or, equivalently $|-28-19|=47^{\circ}$
$10^{\circ}$ with a 25 mph wind and $20^{\circ}$ with a 20 mph wind

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Problem 98

The wind-chill factor, shown in the table, calculates how a given temperature feels to a person's skin when the wind is taken into account. For example, the table shows that a temperature of 20 in a 40 mph wind feels like $-1 .^{\text {at }}$
(TABLE CANNOT COPY)
Find the absolute value of the difference of the two given wind-chill factors. For example, the difference between the wind-chill at 30 with a 15 mph wind and one at
-10 with a 10 mph wind is $|19-(-28)|=47^{\circ}$ or, equivalently $|-28-19|=47^{\circ}$
$30^{\circ}$ with a 10 mph wind and $10^{\circ}$ with a 30 mph wind

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Problem 99

The wind-chill factor, shown in the table, calculates how a given temperature feels to a person's skin when the wind is taken into account. For example, the table shows that a temperature of 20 in a 40 mph wind feels like $-1 .^{\text {at }}$
(TABLE CANNOT COPY)
Find the absolute value of the difference of the two given wind-chill factors. For example, the difference between the wind-chill at 30 with a 15 mph wind and one at
-10 with a 10 mph wind is $|19-(-28)|=47^{\circ}$ or, equivalently $|-28-19|=47^{\circ}$
$-30^{\circ}$ with a $5 \mathrm{mph}$ wind and $0^{\circ}$ with a $10 \mathrm{mph}$ wind

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Problem 100

The graph shows the number of Schedule $C$ and $C$ -EZ forms (in millions) that were filed with the IRS over a six year period.
(GRAPH CANNOT COPY)
In what years was the following statement true:
$$|x-19,500,000| \geq 600,000$$
where $x$ is the number of Schedule $\mathrm{C}$ and C-EZ forms in that year?

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Problem 101

Write the given expression without using absolute values.
$$\left|t^{2}\right|$$

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Problem 102

Write the given expression without using absolute values.
$$\left|-2-y^{2}\right|$$

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Problem 103

Write the given expression without using absolute values.
$$|b-3| \text { if } b \geq 3$$

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Problem 104

Write the given expression without using absolute values.
$$|a-5| \text { if } a<5$$

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Problem 105

Write the given expression without using absolute values.
$$|c-d| \text { if } c<d$$

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Problem 106

Write the given expression without using absolute values.
$$|c-d| \text { if } c \geq d$$

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Problem 107

Write the given expression without using absolute values.
$$|u-v|-|v-u|$$

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Problem 108

Write the given expression without using absolute values.
$$\frac{|u-v|}{|v-u|} \text { if } u \neq v, u \neq 0, v \neq 0$$

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Problem 109

Explain why the given statement is true for any numbers $c$ and $d .$ I Hint: Look at the properties of absolute value on page 10.1
$$\left|(c-d)^{2}\right|=c^{2}-2 c d+d^{2}$$

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Problem 110

Explain why the given statement is true for any numbers $c$ and $d .$ I Hint: Look at the properties of absolute value on page 10.1
$$\sqrt{9 c^{2}-18 c d+9 d^{2}}=3|c-d|$$

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Problem 111

Express the given geometric statement about numbers on the number line algebraically, using absolute values.
The distance from $x$ to 5 is less than 4

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Problem 112

Express the given geometric statement about numbers on the number line algebraically, using absolute values.
is more than 6 units from $c$

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Problem 113

Express the given geometric statement about numbers on the number line algebraically, using absolute values.
$x$ is at most 17 units from -4

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Problem 114

Express the given geometric statement about numbers on the number line algebraically, using absolute values.
$x$ is within 3 units of 7

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Problem 115

Express the given geometric statement about numbers on the number line algebraically, using absolute values.
$c$ is closer to 0 than $b$ is.

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Problem 116

Express the given geometric statement about numbers on the number line algebraically, using absolute values.
$x$ is closer to 1 than to 4

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Problem 117

Translate the given algebraic statement into a geometric statement about numbers on the number line.
$$|x-3|<2$$

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Problem 118

Translate the given algebraic statement into a geometric statement about numbers on the number line.
$$|x-c|>6$$

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Problem 119

Translate the given algebraic statement into a geometric statement about numbers on the number line.
$$|x+7| \leq 3$$

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Problem 120

Translate the given algebraic statement into a geometric statement about numbers on the number line.
$$|u+v| \geq 2$$

Amy Jiang

Numerade Educator

Problem 121

Match each of the following graphs with the appropriate absolute value equation or inequality.
i. $|x-17|=7$
ii. $|x-17|=-7$
iii. $|x-17| \leq 7$
iv. $|x-17| \geq-7$
v. $|x-17|>7$
(a to e, NUMBER LINE CANNOT COPY)

Amy Jiang

Numerade Educator

Problem 122

Explain geometrically why this statement is always false:
$|c-1|<2$ and simultaneously $|c-12|<3$

Amy Jiang

Numerade Educator

Problem 123

Use the geometric approach explained in the text to solve the given equation or inequality.
$$|x|=1$$

Amy Jiang

Numerade Educator

Problem 124

Use the geometric approach explained in the text to solve the given equation or inequality.
$$|x|=3 / 2$$

Amy Jiang

Numerade Educator

Problem 125

Use the geometric approach explained in the text to solve the given equation or inequality.
$$|x-2|=1$$

Amy Jiang

Numerade Educator

Problem 126

Use the geometric approach explained in the text to solve the given equation or inequality.
$$|x+3|=2$$

Amy Jiang

Numerade Educator

Problem 127

Use the geometric approach explained in the text to solve the given equation or inequality.
$$|x+\pi|=4$$

Amy Jiang

Numerade Educator

Problem 128

Use the geometric approach explained in the text to solve the given equation or inequality.
$$\left|x-\frac{3}{2}\right|=5$$

Amy Jiang

Numerade Educator

Problem 129

Use the geometric approach explained in the text to solve the given equation or inequality.
$$|x|<7$$

Amy Jiang

Numerade Educator

Problem 130

Use the geometric approach explained in the text to solve the given equation or inequality.
$$|x| \geq 5$$

Amy Jiang

Numerade Educator

Problem 131

Use the geometric approach explained in the text to solve the given equation or inequality.
$$|x-5|<2$$

Amy Jiang

Numerade Educator

Problem 132

Use the geometric approach explained in the text to solve the given equation or inequality.
$$|x-6|>2$$

Amy Jiang

Numerade Educator

Problem 133

Use the geometric approach explained in the text to solve the given equation or inequality.
$$|x+2| \geq 3$$

Amy Jiang

Numerade Educator

Problem 134

Use the geometric approach explained in the text to solve the given equation or inequality.
$$|x+4| \leq 2$$

Amy Jiang

Numerade Educator

Problem 135

Explain why the statement $|a|+|b|+|c|>0$ is algebraic shorthand for "at least one of the numbers $a, b, c,$ is different from zero."

Amy Jiang

Numerade Educator

Problem 136

Find an algebraic shorthand version of the statement "none of the numbers $a, b, c,$ is zero."

Amy Jiang

Numerade Educator