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Introductory and Intermediate Algebra for College Students 4th

Robert Blitzer

Chapter 2

Linear Equations and Inequalities in One Variable - all with Video Answers

Educators

Section 1

The Addition Property of Equality

01:24

Problem 1

Identify the linear equations in one variable.
$$x-9=13$$

Aryan Malesha
Aryan Malesha
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00:35

Problem 2

Identify the linear equations in one variable.
$$x-15=20$$

Sophia Rafiqi
Sophia Rafiqi
Numerade Educator
02:10

Problem 3

Identify the linear equations in one variable.
$$x^{2}-9=13$$

Aryan Malesha
Aryan Malesha
Numerade Educator
00:50

Problem 4

Identify the linear equations in one variable.
$$x^{2}-15=20$$

Sophia Rafiqi
Sophia Rafiqi
Numerade Educator
01:25

Problem 5

Identify the linear equations in one variable.
$$\frac{9}{x}=13$$

Aryan Malesha
Aryan Malesha
Numerade Educator
02:20

Problem 6

Identify the linear equations in one variable.
$$\frac{15}{x}=20$$

Willis James
Willis James
Numerade Educator
02:33

Problem 7

Identify the linear equations in one variable.
$$\sqrt{2} x+\pi=0 . \overline{3}$$

Aryan Malesha
Aryan Malesha
Numerade Educator
01:44

Problem 8

Identify the linear equations in one variable.
$$\sqrt{3} x+\pi=0 . \overline{6}$$

Sophia Rafiqi
Sophia Rafiqi
Numerade Educator
02:12

Problem 9

Identify the linear equations in one variable.
$$|x+2|=5$$

Aryan Malesha
Aryan Malesha
Numerade Educator
01:56

Problem 10

Identify the linear equations in one variable.
$$|x+5|=8$$

Sophia Rafiqi
Sophia Rafiqi
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01:09

Problem 11

Solve each equation. Using the addition property of equality. Be sure to check your proposed solutions.
$$x-4=19$$

Aryan Malesha
Aryan Malesha
Numerade Educator
00:58

Problem 12

Solve each equation. Using the addition property of equality. Be sure to check your proposed solutions.
$$y-5=-18$$

Sophia Rafiqi
Sophia Rafiqi
Numerade Educator
01:19

Problem 13

Solve each equation. Using the addition property of equality. Be sure to check your proposed solutions.
$$z+8=-12$$

Aryan Malesha
Aryan Malesha
Numerade Educator
01:06

Problem 14

Solve each equation. Using the addition property of equality. Be sure to check your proposed solutions.
$$z+13=-15$$

Sophia Rafiqi
Sophia Rafiqi
Numerade Educator
01:23

Problem 15

Solve each equation. Using the addition property of equality. Be sure to check your proposed solutions.
$$-2=x+14$$

Aryan Malesha
Aryan Malesha
Numerade Educator
00:44

Problem 16

Solve each equation. Using the addition property of equality. Be sure to check your proposed solutions.
$$-13=x+11$$

Sophia Rafiqi
Sophia Rafiqi
Numerade Educator
01:18

Problem 17

Solve each equation. Using the addition property of equality. Be sure to check your proposed solutions.
$$-17=y-5$$

Aryan Malesha
Aryan Malesha
Numerade Educator
00:36

Problem 18

Solve each equation. Using the addition property of equality. Be sure to check your proposed solutions.
$$-21=y-4$$

Sophia Rafiqi
Sophia Rafiqi
Numerade Educator
01:18

Problem 19

Solve each equation. Using the addition property of equality. Be sure to check your proposed solutions.
$$7+z=11$$

Aryan Malesha
Aryan Malesha
Numerade Educator
00:39

Problem 20

Solve each equation. Using the addition property of equality. Be sure to check your proposed solutions.
$$18+z=14$$

Sophia Rafiqi
Sophia Rafiqi
Numerade Educator
01:20

Problem 21

Solve each equation. Using the addition property of equality. Be sure to check your proposed solutions.
$$-6+y=-17$$

Aryan Malesha
Aryan Malesha
Numerade Educator
00:36

Problem 22

Solve each equation. Using the addition property of equality. Be sure to check your proposed solutions.
$$-8+y=-29$$

Sophia Rafiqi
Sophia Rafiqi
Numerade Educator
01:47

Problem 23

Solve each equation. Using the addition property of equality. Be sure to check your proposed solutions.
$$x+\frac{1}{3}=\frac{7}{3}$$

Aryan Malesha
Aryan Malesha
Numerade Educator
01:07

Problem 24

Solve each equation. Using the addition property of equality. Be sure to check your proposed solutions.
$$x+\frac{7}{8}=\frac{9}{8}$$

Sophia Rafiqi
Sophia Rafiqi
Numerade Educator
02:49

Problem 25

Solve each equation. Using the addition property of equality. Be sure to check your proposed solutions.
$$t+\frac{5}{6}=-\frac{7}{12}$$

Aryan Malesha
Aryan Malesha
Numerade Educator
01:34

Problem 26

Solve each equation. Using the addition property of equality. Be sure to check your proposed solutions.
$$t+\frac{2}{3}=-\frac{7}{6}$$

Sophia Rafiqi
Sophia Rafiqi
Numerade Educator
01:44

Problem 27

Solve each equation. Using the addition property of equality. Be sure to check your proposed solutions.
$$x-\frac{3}{4}=\frac{9}{2}$$

Aryan Malesha
Aryan Malesha
Numerade Educator
01:34

Problem 28

Solve each equation. Using the addition property of equality. Be sure to check your proposed solutions.
$$x-\frac{3}{5}=\frac{7}{10}$$

Sophia Rafiqi
Sophia Rafiqi
Numerade Educator
02:52

Problem 29

Solve each equation. Using the addition property of equality. Be sure to check your proposed solutions.
$$-\frac{1}{5}+y=-\frac{3}{4}$$

Aryan Malesha
Aryan Malesha
Numerade Educator
01:31

Problem 30

Solve each equation. Using the addition property of equality. Be sure to check your proposed solutions.
$$-\frac{1}{8}+y=-\frac{1}{4}$$

Sophia Rafiqi
Sophia Rafiqi
Numerade Educator
02:13

Problem 31

Solve each equation. Using the addition property of equality. Be sure to check your proposed solutions.
$$3.2+x=7.5$$

Aryan Malesha
Aryan Malesha
Numerade Educator
00:37

Problem 32

Solve each equation. Using the addition property of equality. Be sure to check your proposed solutions.
$$-2.7+w=-5.3$$

Sophia Rafiqi
Sophia Rafiqi
Numerade Educator
02:35

Problem 33

Solve each equation. Using the addition property of equality. Be sure to check your proposed solutions.
$$x+\frac{3}{4}=-\frac{9}{2}$$

Aryan Malesha
Aryan Malesha
Numerade Educator
01:44

Problem 34

Solve each equation. Using the addition property of equality. Be sure to check your proposed solutions.
$$r+\frac{3}{5}=-\frac{7}{10}$$

Sophia Rafiqi
Sophia Rafiqi
Numerade Educator
01:22

Problem 35

Solve each equation. Using the addition property of equality. Be sure to check your proposed solutions.
$$5=-13+y$$

Aryan Malesha
Aryan Malesha
Numerade Educator
00:28

Problem 36

Solve each equation. Using the addition property of equality. Be sure to check your proposed solutions.
$$-11=8+x$$

Sophia Rafiqi
Sophia Rafiqi
Numerade Educator
02:47

Problem 37

Solve each equation. Using the addition property of equality. Be sure to check your proposed solutions.
$$-\frac{3}{5}=-\frac{3}{2}+s$$

Aryan Malesha
Aryan Malesha
Numerade Educator
01:42

Problem 38

Solve each equation. Using the addition property of equality. Be sure to check your proposed solutions.
$$\frac{7}{3}=-\frac{5}{2}+z$$

Sophia Rafiqi
Sophia Rafiqi
Numerade Educator
01:53

Problem 39

Solve each equation. Using the addition property of equality. Be sure to check your proposed solutions.
$$830+y=520$$

Aryan Malesha
Aryan Malesha
Numerade Educator
00:33

Problem 40

Solve each equation. Using the addition property of equality. Be sure to check your proposed solutions.
$$-90+t=-35$$

Sophia Rafiqi
Sophia Rafiqi
Numerade Educator
02:17

Problem 41

Solve each equation. Using the addition property of equality. Be sure to check your proposed solutions.
$$r+3.7=8$$

Aryan Malesha
Aryan Malesha
Numerade Educator
00:34

Problem 42

Solve each equation. Using the addition property of equality. Be sure to check your proposed solutions.
$$x+10.6=-9$$

Sophia Rafiqi
Sophia Rafiqi
Numerade Educator
01:30

Problem 43

Solve each equation. Using the addition property of equality. Be sure to check your proposed solutions.
$$-3.7+m=-3.7$$

Aryan Malesha
Aryan Malesha
Numerade Educator
00:47

Problem 44

Solve each equation. Using the addition property of equality. Be sure to check your proposed solutions.
$$y+\frac{7}{11}=\frac{7}{11}$$

Sophia Rafiqi
Sophia Rafiqi
Numerade Educator
01:36

Problem 45

Solve each equation. Using the addition property of equality. Be sure to check your proposed solutions.
$$6 y+3-5 y=14$$

Aryan Malesha
Aryan Malesha
Numerade Educator
01:07

Problem 46

Solve each equation. Using the addition property of equality. Be sure to check your proposed solutions.
$$-3 x-5+4 x=9$$

Sophia Rafiqi
Sophia Rafiqi
Numerade Educator
03:54

Problem 47

Solve each equation. Using the addition property of equality. Be sure to check your proposed solutions.
$$7-5 x+8+2 x+4 x-3=2+3 \cdot 5$$

Aryan Malesha
Aryan Malesha
Numerade Educator
02:36

Problem 48

Solve each equation. Using the addition property of equality. Be sure to check your proposed solutions.
$$13-3 r+2+6 r-2 r-1=3+2 \cdot 9$$

Sophia Rafiqi
Sophia Rafiqi
Numerade Educator
02:38

Problem 49

Solve each equation. Using the addition property of equality. Be sure to check your proposed solutions.
$$7 y+4=6 y-9$$

Aryan Malesha
Aryan Malesha
Numerade Educator
01:00

Problem 50

Solve each equation. Using the addition property of equality. Be sure to check your proposed solutions.
$$4 r-3=5+3 r$$

Sophia Rafiqi
Sophia Rafiqi
Numerade Educator
02:16

Problem 51

Solve each equation. Using the addition property of equality. Be sure to check your proposed solutions.
$$12-6 x=18-7 x$$

Aryan Malesha
Aryan Malesha
Numerade Educator
00:59

Problem 52

Solve each equation. Using the addition property of equality. Be sure to check your proposed solutions.
$$20-7 s=26-8 s$$

Sophia Rafiqi
Sophia Rafiqi
Numerade Educator
02:47

Problem 53

Solve each equation. Using the addition property of equality. Be sure to check your proposed solutions.
$$4 x+2=3(x-6)+8$$

Aryan Malesha
Aryan Malesha
Numerade Educator
01:23

Problem 54

Solve each equation. Using the addition property of equality. Be sure to check your proposed solutions.
$$7 x+3=6(x-1)+9$$

Sophia Rafiqi
Sophia Rafiqi
Numerade Educator
01:14

Problem 55

The equations in Exercises $55-58$ contain small geometric figures that represent real numbers. Use the addition property
of equality to isolate $x$ on one side of the equation and the geometric figures on the other side.
$$x-\square=\triangle$$

Aryan Malesha
Aryan Malesha
Numerade Educator
00:41

Problem 56

Contain small geometric figures that represent real numbers. Use the addition property of equality to isolate $x$ on one side of the equation and the geometric figures on the other side.
$$x+\square=\Delta$$

Sophia Rafiqi
Sophia Rafiqi
Numerade Educator
01:24

Problem 57

Contain small geometric figures that represent real numbers. Use the addition property of equality to isolate $x$ on one side of the equation and the geometric figures on the other side.
$$2 x+\Delta=3 x+\square$$

Aryan Malesha
Aryan Malesha
Numerade Educator
01:46

Problem 58

Contain small geometric figures that represent real numbers. Use the addition property of equality to isolate $x$ on one side of the equation and the geometric figures on the other side.
$$6 x-\Delta=7 x-\square$$

Sophia Rafiqi
Sophia Rafiqi
Numerade Educator
00:51

Problem 59

Use the given information to write an equation. Let $x$ represent the number described in each exercise. Then solve the equation and find the number.
If 12 is subtracted from a number, the result is $-2 .$ Find the number.

Aryan Malesha
Aryan Malesha
Numerade Educator
00:53

Problem 60

Use the given information to write an equation. Let $x$ represent the number described in each exercise. Then solve the equation and find the number.
If 23 is subtracted from a number, the result is $-8 .$ Find the number.

Sophia Rafiqi
Sophia Rafiqi
Numerade Educator
01:49

Problem 61

Use the given information to write an equation. Let $x$ represent the number described in each exercise. Then solve the equation and find the number.
The difference between $\frac{2}{5}$ of a number and 8 is $\frac{7}{5}$ of that number. Find the number.

Aryan Malesha
Aryan Malesha
Numerade Educator
03:22

Problem 62

Use the given information to write an equation. Let $x$ represent the number described in each exercise. Then solve the equation and find the number.
The difference between 3 and $\frac{2}{7}$ of a number is $\frac{5}{4}$ of that number. Find the number.

Sophia Rafiqi
Sophia Rafiqi
Numerade Educator
01:31

Problem 63

Formulas frequently appear in the business world. For example, the cost, $C,$ of an item (the price paid by a retailer) plus the markup, $M,$ on that item (the retailer's profit) equals the selling price, $S,$ of the item. The formula is
$$C+M=S$$
The selling price of a computer is $\$ 1850 .$ If the markup on the computer is $\$ 150,$ find the cost to the retailer for the computer.

Aryan Malesha
Aryan Malesha
Numerade Educator
01:47

Problem 64

Formulas frequently appear in the business world. For example, the cost, $C,$ of an item (the price paid by a retailer) plus the markup, $M,$ on that item (the retailer's profit) equals the selling price, $S,$ of the item. The formula is
$$C+M=S$$
The selling price of a television is $\$ 650 .$ If the cost to the retailer for the television is $\$ 520,$ find the markup.

Sophia Rafiqi
Sophia Rafiqi
Numerade Educator
01:23

Problem 65

The bar graph shows the average credit-card debt per $U . S$. household for selected years from 2000 through 2008
(GRAPH CANNOT COPY)
The data displayed by the bar graph can be described by the mathematical model
$$d-257 x=8328$$
where $d$ is the average credit-card debt per U.S. household $x$ years after $2000 .$
According to the formula at the bottom of the previous column, what was the average credit-card debt per U.S. household for $2008 ?$ Does this underestimate or overestimate the number displayed by the bar graph? By how much?

Amanda Tricario
Amanda Tricario
Numerade Educator
01:23

Problem 66

The bar graph shows the average credit-card debt per $U . S$. household for selected years from 2000 through 2008
(GRAPH CANNOT COPY)
The data displayed by the bar graph can be described by the mathematical model
$$d-257 x=8328$$
where $d$ is the average credit-card debt per U.S. household $x$ years after $2000 .$
According to the formula at the bottom of the previous column, what was the average credit-card debt per U.S. household for $2007 ?$ Does this underestimate or overestimate the number displayed by the bar graph? By how much?

Amanda Tricario
Amanda Tricario
Numerade Educator
04:00

Problem 67

The diversity index, from 0 ( no diversity) to Ioo, measures the chance that two randomly selected people are a different race or ethnicity. The diversity index in the United States varies widely from region to region, from as high as 79 in Hawaii and 68 in California to as low as 10 in Maine and Vermont and 13 in West Virginia. The line graph shows the national diversity index for the United States for four years in the period from 1980 through 2009
(GRAPH CANNOT COPY)
The data displayed by the line graph can be described by the mathematical model
$$
I-0.6 x=34
$$
where I is the national diversity index in the United States $x$ years after $1980 .$
a. Use the line graph to estimate the U.S. diversity index in 2009
b. Use the formula to determine the U.S. diversity index in $2009 .$ How does this compare with your graphical esti par

Sophia Rafiqi
Sophia Rafiqi
Numerade Educator
04:00

Problem 68

The diversity index, from 0 ( no diversity) to Ioo, measures the chance that two randomly selected people are a different race or ethnicity. The diversity index in the United States varies widely from region to region, from as high as 79 in Hawaii and 68 in California to as low as 10 in Maine and Vermont and 13 in West Virginia. The line graph shows the national diversity index for the United States for four years in the period from 1980 through 2009
(GRAPH CANNOT COPY)
The data displayed by the line graph can be described by the mathematical model
$$
I-0.6 x=34
$$
where I is the national diversity index in the United States $x$ years after $1980 .$
a. Use the line graph to estimate the U.S. diversity index in 2000
b. Use the formula to determine the U.S. diversity index in $2000 .$ How does this compare with your graphical estimate from part (a)?

Sophia Rafiqi
Sophia Rafiqi
Numerade Educator
01:25

Problem 69

State the addition property of equality and give an example.

Aryan Malesha
Aryan Malesha
Numerade Educator
00:56

Problem 70

Explain why $x+2=9$ and $x+2=-6$ are not equivalent equations.

Sophia Rafiqi
Sophia Rafiqi
Numerade Educator
02:34

Problem 71

What is the difference between solving an equation such as
$$
5 y+3-4 y-8=6+9
$$
and simplifying an algebraic expression such as
$$
5 y+3-4 y-8 ?
$$
If there is a difference, which topic should be taught first? Why?

Aryan Malesha
Aryan Malesha
Numerade Educator
01:12

Problem 72

Look, again, at the graph for Exercises $67-68$ that shows the diversity index in the United States over time. You used a linear equation to solve Exercise 67 or $68 .$ What does the adjective linear have to do with the relationship among the four data points in the graph?

Sophia Rafiqi
Sophia Rafiqi
Numerade Educator
01:41

Problem 73

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning.
The book is teaching me totally different things than my instructor: The book adds the number to both sides beside the equation, but my instructor adds the number underneath.

Aryan Malesha
Aryan Malesha
Numerade Educator
01:01

Problem 74

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning.
There are times that I prefer to check an equation's solution in my head and not show the check.

Sophia Rafiqi
Sophia Rafiqi
Numerade Educator
01:13

Problem 75

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning.
Solving an equation reminds me of keeping a barbell balanced: If I add weight to or subtract weight from one side of the bar, I must do the same thing to the other side.

Aryan Malesha
Aryan Malesha
Numerade Educator
00:57

Problem 76

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning.
I used a linear equation to explore data points lying on the same line.

Sophia Rafiqi
Sophia Rafiqi
Numerade Educator
01:52

Problem 77

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.
If $y-a=-b,$ then $y=a+b$

Aryan Malesha
Aryan Malesha
Numerade Educator
01:35

Problem 78

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.
If $y+7=0,$ then $y=7$

Sophia Rafiqi
Sophia Rafiqi
Numerade Educator
01:08

Problem 79

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.
If $2 x-5=3 x,$ then $x=-5$

Aryan Malesha
Aryan Malesha
Numerade Educator
00:45

Problem 80

If $3 x=18,$ then $x=18-3$

Sophia Rafiqi
Sophia Rafiqi
Numerade Educator
02:17

Problem 81

Write an equation with a negative solution that can be solved by adding 100 to both sides.

Aryan Malesha
Aryan Malesha
Numerade Educator
00:46

Problem 82

Use a calculator to solve each equation.
$$x-7.0463=-9.2714$$

Sophia Rafiqi
Sophia Rafiqi
Numerade Educator
01:24

Problem 83

Use a calculator to solve each equation.
$$6.9825=4.2296+y$$

Aryan Malesha
Aryan Malesha
Numerade Educator
00:41

Problem 84

Write as an algebraic expression in which $x$ represents the number: the quotient of 9 and a number, decreased by
4 times the number. (Section 1.1, Example 3)

Sophia Rafiqi
Sophia Rafiqi
Numerade Educator
01:47

Problem 85

Simplify: $-16-8 \div 4 \cdot(-2) .$ (Section $1.8,$ Example 4 )

Aryan Malesha
Aryan Malesha
Numerade Educator
01:34

Problem 86

Simplify: $3[7 x-2(5 x-1)] .$ (Section 1.8, Example 11)

Sophia Rafiqi
Sophia Rafiqi
Numerade Educator
01:09

Problem 87

Will help you prepare for the material covered in the next section.
Multiply and simplify: $\quad 5 \cdot \frac{x}{5}$

Aryan Malesha
Aryan Malesha
Numerade Educator
00:21

Problem 88

Will help you prepare for the material covered in the next section.
Divide and simplify: $\frac{-7 y}{-7}$

Sophia Rafiqi
Sophia Rafiqi
Numerade Educator
01:09

Problem 89

Will help you prepare for the material covered in the next section.
Is 4 a solution of $3 x-14=-2 x+6 ?$

Aryan Malesha
Aryan Malesha
Numerade Educator