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Precalculus

Margaret L. Lial, John Hornsby, David I. Schneide

Chapter 1

Equations and Inequalities - all with Video Answers

Educators

Section 1

Linear Equations

01:04

Problem 1

$A(n)$ _________ is a statement that two expressions are equal.

Julie Silva
Julie Silva
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01:04

Problem 2

To ________ an equation means to find all numbers that make the equation a true
statement.

Julie Silva
Julie Silva
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01:06

Problem 3

A linear equation is a(n) ______ because the greatest degree of the variable is 1.

Julie Silva
Julie Silva
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01:07

Problem 4

A(n) __________ is an equation satisfied by every number that is a meaningful replacement for the variable.

Julie Silva
Julie Silva
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01:11

Problem 5

A(n) _______ is an equation that has no solution.

Julie Silva
Julie Silva
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01:06

Problem 6

Decide whether each statement is true or false.
The solution set of $2 x+5=x-3$ is $\{-8\}$

Sarah X
Sarah X
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00:52

Problem 7

Decide whether each statement is true or false.
The equation $5(x-8)=5 x-40$ is an example of an identity.

Sarah X
Sarah X
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01:08

Problem 8

Decide whether each statement is true or false.
The equation $5 x=4 x$ is an example of a contradiction.

Julie Silva
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01:07

Problem 9

Decide whether each statement is true or false.
Solving the literal equation $A=\frac{1}{2} b h$ for the variable $h$ gives $h=\frac{A}{2 b}$

Julie Silva
Julie Silva
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01:12

Problem 10

Which one is not a linear equation?
A. $5 x+7(x-1)=-3 x$
B. $9 x^{2}-4 x+3=0$
C. $7 x+8 x=13 x$
D. $0.04 x-0.08 x=0.40$

Sarah X
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01:06

Problem 11

Solve each equation. See Examples 1 and 2.
$$5 x+4=3 x-4$$

Julie Silva
Julie Silva
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01:08

Problem 12

Solve each equation. See Examples 1 and 2.
$$9 x+11=7 x+1$$

Julie Silva
Julie Silva
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01:20

Problem 13

Solve each equation. See Examples 1 and 2.
$$6(3 x-1)=8-(10 x-14)$$

Julie Silva
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01:25

Problem 14

Solve each equation. See Examples 1 and 2.
$$4(-2 x+1)=6-(2 x-4)$$

Julie Silva
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01:12

Problem 15

Solve each equation. See Examples 1 and 2.
$$\frac{5}{6} x-2 x+\frac{4}{3}=\frac{5}{3}$$

Julie Silva
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01:19

Problem 16

Solve each equation. See Examples 1 and 2.
$$\frac{7}{4}+\frac{1}{5} x-\frac{3}{2}=\frac{4}{5} x$$

Julie Silva
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01:12

Problem 17

Solve each equation. See Examples 1 and 2.
$$3 x+5-5(x+1)=6 x+7$$

Julie Silva
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01:32

Problem 18

Solve each equation. See Examples 1 and 2.
$$5(x+3)+4 x-3=-(2 x-4)+2$$

Julie Silva
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01:32

Problem 19

Solve each equation. See Examples 1 and 2.
$$2[x-(4+2 x)+3]=2 x+2$$

Julie Silva
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01:37

Problem 20

Solve each equation. See Examples 1 and 2.
$$4[2 x-(3-x)+5]=-6 x-28$$

Julie Silva
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01:28

Problem 21

Solve each equation. See Examples 1 and 2.
$$\frac{1}{14}(3 x-2)=\frac{x+10}{10}$$

Julie Silva
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01:33

Problem 22

Solve each equation. See Examples 1 and 2.
$$\frac{1}{15}(2 x+5)=\frac{x+2}{9}$$

Julie Silva
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01:04

Problem 23

Solve each equation. See Examples 1 and 2.
$$0.2 x-0.5=0.1 x+7$$

Julie Silva
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01:41

Problem 24

Solve each equation. See Examples 1 and 2.
$$0.01 x+3.1=2.03 x-2.96$$

Julie Silva
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01:04

Problem 25

Solve each equation. See Examples 1 and 2.
$$-4(2 x-6)+8 x=5 x+24+x$$

Julie Silva
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01:33

Problem 26

Solve each equation. See Examples 1 and 2.
$$-8(3 x+4)+6 x=4(x-8)+4 x$$

Julie Silva
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01:11

Problem 27

Solve each equation. See Examples 1 and 2.
$$0.5 x+\frac{4}{3} x=x+10$$

Julie Silva
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01:18

Problem 28

Solve each equation. See Examples 1 and 2.
$$\frac{2}{3} x+0.25 x=x+2$$

Julie Silva
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01:34

Problem 29

Solve each equation. See Examples 1 and 2.
$$0.08 x+0.06(x+12)=7.72$$

Julie Silva
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01:25

Problem 30

Solve each equation. See Examples 1 and 2.
$$0.04(x-12)+0.06 x=1.52$$

Julie Silva
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01:19

Problem 31

Determine whether each equation is an identity, a conditional equation, or a contradiction. Give the solution set.
$$4(2 x+7)=2 x+22+3(2 x+2)$$

Julie Silva
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01:13

Problem 32

Determine whether each equation is an identity, a conditional equation, or a contradiction. Give the solution set.
$$\frac{1}{2}(6 x+20)=x+4+2(x+3)$$

Julie Silva
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01:16

Problem 33

Determine whether each equation is an identity, a conditional equation, or a contradiction. Give the solution set.
$$2(x-8)=3 x-16$$

Julie Silva
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01:35

Problem 34

Determine whether each equation is an identity, a conditional equation, or a contradiction. Give the solution set.
$$-8(x+5)=-8 x-5(x+8)$$

Julie Silva
Julie Silva
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01:25

Problem 35

Determine whether each equation is an identity, a conditional equation, or a contradiction. Give the solution set.
$$4(x+7)=2(x+12)+2(x+1)$$

Julie Silva
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01:31

Problem 36

Determine whether each equation is an identity, a conditional equation, or a contradiction. Give the solution set.
$$-6(2 x+1)-3(x-4)=-15 x+1$$

Julie Silva
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01:49

Problem 37

Determine whether each equation is an identity, a conditional equation, or a contradiction. Give the solution set.
$$0.3(x+2)-0.5(x+2)=-0.2 x-0.4$$

Julie Silva
Julie Silva
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01:46

Problem 38

Determine whether each equation is an identity, a conditional equation, or a contradiction. Give the solution set.
$$-0.6(x-5)+0.8(x-6)=0.2 x-1.8$$

Julie Silva
Julie Silva
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01:06

Problem 39

Solve each formula for the specified variable. Assume that the denominator is not 0 if variables appear in the denominator. See Examples 4(a) and (b).
$V=l w h, \quad$ for $l \quad$ (volume of a rectangular box)

Julie Silva
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01:05

Problem 40

Solve each formula for the specified variable. Assume that the denominator is not 0 if variables appear in the denominator. See Examples 4(a) and (b).
$I=P r t, \quad$ for $P \quad$ (simple interest)

Julie Silva
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01:10

Problem 41

Solve each formula for the specified variable. Assume that the denominator is not 0 if variables appear in the denominator. See Examples 4(a) and (b).
$P=a+b+c, \quad$ for $c \quad$ (perimeter of a triangle)

Julie Silva
Julie Silva
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01:12

Problem 42

Solve each formula for the specified variable. Assume that the denominator is not 0 if variables appear in the denominator. See Examples 4(a) and (b).
$P=2 l+2 w, \quad$ for $w \quad(\text { perimeter of a rectangle })$

Julie Silva
Julie Silva
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01:11

Problem 43

Solve each formula for the specified variable. Assume that the denominator is not 0 if variables appear in the denominator. See Examples 4(a) and (b).
$\mathscr{A}=\frac{1}{2} h(B+b), \quad$ for $B \quad$ (area of a trapezoid)

Julie Silva
Julie Silva
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01:10

Problem 44

Solve each formula for the specified variable. Assume that the denominator is not 0 if variables appear in the denominator. See Examples 4(a) and (b).
$\mathscr{A}=\frac{1}{2} h(B+b), \quad$ for $h \quad$ (area of a trapezoid)

Julie Silva
Julie Silva
Numerade Educator
01:17

Problem 45

Solve each formula for the specified variable. Assume that the denominator is not 0 if variables appear in the denominator. See Examples 4(a) and (b).
$S=2 \pi r h+2 \pi r^{2}, \quad$ for $h \quad$ (surface area of a right circular cylinder)

Julie Silva
Julie Silva
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01:06

Problem 46

Solve each formula for the specified variable. Assume that the denominator is not 0 if variables appear in the denominator. See Examples 4(a) and (b).
$s=\frac{1}{2} g t^{2}, \quad$ for $g \quad$ (distance traveled by a falling object)

Julie Silva
Julie Silva
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01:22

Problem 47

Solve each formula for the specified variable. Assume that the denominator is not 0 if variables appear in the denominator. See Examples 4(a) and (b).
$S=2 l w+2 w h+2 h l, \quad$ for $h \quad(\text { surface area of a rectangular box })$

Julie Silva
Julie Silva
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01:06

Problem 48

Solve each formula for the specified variable. Assume that the denominator is not 0 if variables appear in the denominator. See Examples 4(a) and (b).
$z=\frac{x-\mu}{\sigma},$ for $x \quad$ (standardized value)

Julie Silva
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01:06

Problem 49

Solve each equation for $x .$ See Example $4(c)$
$$2(x-a)+b=3 x+a$$

Julie Silva
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01:23

Problem 50

Solve each equation for $x .$ See Example $4(c)$
$$5 x-(2 a+c)=4(x+c)$$

Julie Silva
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01:17

Problem 51

Solve each equation for $x .$ See Example $4(c)$
$$a x+b=3(x-a)$$

Julie Silva
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01:16

Problem 52

Solve each equation for $x .$ See Example $4(c)$
$$4 a-a x=3 b+b x$$

Julie Silva
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01:40

Problem 53

Solve each equation for $x .$ See Example $4(c)$
$$\frac{x}{a-1}=a x+3$$

Julie Silva
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01:32

Problem 54

Solve each equation for $x .$ See Example $4(c)$
$$\frac{x-1}{2 a}=2 x-a$$

Julie Silva
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01:07

Problem 55

Solve each equation for $x .$ See Example $4(c)$
$$a^{2} x+3 x=2 a^{2}$$

Julie Silva
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01:16

Problem 56

Solve each equation for $x .$ See Example $4(c)$
$$a x+b^{2}=b x-a^{2}$$

Julie Silva
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01:38

Problem 57

Solve each equation for $x .$ See Example $4(c)$
$$3 x=(2 x-1)(m+4)$$

Julie Silva
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01:55

Problem 58

Solve each equation for $x .$ See Example $4(c)$
$$-x=(5 x+3)(3 k+1)$$

Julie Silva
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01:45

Problem 59

Elmer borrowed $\$ 3150$ from his brother Julio to pay for books and tuition. He agreed to repay Julio in 6 months with simple annual interest at 4\%.
(a) How much will the interest amount to?
(b) What amount must Elmer pay Julio at the end of the 6 months?

Mukesh Devi
Mukesh Devi
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02:20

Problem 60

Levada borrows $\$ 30,900$ from her bank to open a florist shop. She agrees to repay the money in 18 months with simple annual interest of $5.5 \%$
(a) How much must she pay the bank in 18 months?
(b) How much of the amount in part (a) is interest?

Julie Silva
Julie Silva
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01:07

Problem 61

In the metric system of weights and measures, temperature is measured in degrees Celsius ("C) instead of degrees Fahrenheit ( $^{\circ} \mathrm{F}$ ). To convert between the two systems, we use the equations
$$C=\frac{5}{9}(F-32) \text { and } F=\frac{9}{5} C+32$$
In each exercise, convert to the other system. Round answers to the nearest tenth of a degree if necessary.
$$20^{\circ} \mathrm{C}$$

Julie Silva
Julie Silva
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01:02

Problem 62

In the metric system of weights and measures, temperature is measured in degrees Celsius ("C) instead of degrees Fahrenheit ( $^{\circ} \mathrm{F}$ ). To convert between the two systems, we use the equations
$$C=\frac{5}{9}(F-32) \text { and } F=\frac{9}{5} C+32$$
In each exercise, convert to the other system. Round answers to the nearest tenth of a degree if necessary.
$$200^{\circ} \mathrm{C}$$

Julie Silva
Julie Silva
Numerade Educator
01:03

Problem 63

In the metric system of weights and measures, temperature is measured in degrees Celsius ("C) instead of degrees Fahrenheit ( $^{\circ} \mathrm{F}$ ). To convert between the two systems, we use the equations
$$C=\frac{5}{9}(F-32) \text { and } F=\frac{9}{5} C+32$$
In each exercise, convert to the other system. Round answers to the nearest tenth of a degree if necessary.
$$50^{\circ} \mathrm{F}$$

Julie Silva
Julie Silva
Numerade Educator
01:08

Problem 64

In the metric system of weights and measures, temperature is measured in degrees Celsius ("C) instead of degrees Fahrenheit ( $^{\circ} \mathrm{F}$ ). To convert between the two systems, we use the equations
$$C=\frac{5}{9}(F-32) \text { and } F=\frac{9}{5} C+32$$
In each exercise, convert to the other system. Round answers to the nearest tenth of a degree if necessary.
$$77^{\circ} \mathrm{F}$$

Julie Silva
Julie Silva
Numerade Educator
01:09

Problem 65

In the metric system of weights and measures, temperature is measured in degrees Celsius ("C) instead of degrees Fahrenheit ( $^{\circ} \mathrm{F}$ ). To convert between the two systems, we use the equations
$$C=\frac{5}{9}(F-32) \text { and } F=\frac{9}{5} C+32$$
In each exercise, convert to the other system. Round answers to the nearest tenth of a degree if necessary.
$$100^{\circ} \mathrm{F}$$

Julie Silva
Julie Silva
Numerade Educator
01:15

Problem 66

In the metric system of weights and measures, temperature is measured in degrees Celsius ("C) instead of degrees Fahrenheit ( $^{\circ} \mathrm{F}$ ). To convert between the two systems, we use the equations
$$C=\frac{5}{9}(F-32) \text { and } F=\frac{9}{5} C+32$$
In each exercise, convert to the other system. Round answers to the nearest tenth of a degree if necessary.
$$350^{\circ} \mathrm{F}$$

Julie Silva
Julie Silva
Numerade Educator
01:09

Problem 67

Work each problem. Round to the nearest tenth of a degree, if necessary.
Temperature of Venus Venus is the hottest planet, with a surface temperature of $867^{\circ} \mathrm{F}$. What is this temperature in Celsius? (Source: World Almanac and Book of Facts.

Julie Silva
Julie Silva
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01:19

Problem 68

Work each problem. Round to the nearest tenth of a degree, if necessary.
Temperature at Soviet Antarctica Station A record low temperature of $-89.4^{\circ} \mathrm{C}$ was recorded at the Soviet Antarctica Station of Vostok on July $21,1983 .$ Find the corresponding Fahrenheit temperature. (Source: World Almanac and Book of Facts.)

Julie Silva
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01:03

Problem 69

Work each problem. Round to the nearest tenth of a degree, if necessary.
Temperature in South Carolina A record high temperature of $113^{\circ} \mathrm{F}$ was recorded for the state of South Carolina on June $29,2012$. What is the corresponding Celsius temperature? (Source: U.S. National Oceanic and Atmospheric Administration.)

Julie Silva
Julie Silva
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01:09

Problem 70

Work each problem. Round to the nearest tenth of a degree, if necessary.
Temperature in Haiti The average annual temperature in Port-au-Prince, Haiti, is approximately $28.1^{\circ} \mathrm{C} .$ What is the corresponding Fahrenheit temperature?

Julie Silva
Julie Silva
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