Beginning and Intermediate Algebra

Julie Miller,Molly O’Neill,Nancy Hyde

Chapter 2

Linear Equations and Inequalities - all with Video Answers

Educators

Section 1

Addition, Subtraction, Multiplication, and Division Properties of Equality

Problem 1

After getting a test back, it is a good idea to correct the test so that you do not make the same errors again. One recommended approach is to use a clean sheet of paper, and divide the paper down the middle vertically as shown. For each problem that you missed on the test, rework the problem correctly on the lefthand side of the paper. Then give a written explanation on the right-hand side of the paper. To reinforce the correct procedure, do four more problems of that type.
Take the time this week to make corrections from your last test.

Brandon Fox

Brandon Fox

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Problem 2

Define the key terms.
a. linear equation in one variable
b. solution to an equation
c. solution set
d. addition property of equality
e. subtraction property of equality
f. multiplication property of equality

Khanh Ha

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Problem 3

Identify the following as either an expression or an equation.
$$x-4+5 x$$

Brandon Fox

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Problem 4

Identify the following as either an expression or an equation.
$$8 x+2=7$$

Brandon Fox

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Problem 5

Identify the following as either an expression or an equation.
$$9=2 x-4$$

Brandon Fox

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Problem 6

Identify the following as either an expression or an equation.
$$3 x^{2}+x=-3$$

Brandon Fox

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Problem 7

Identify the following as either an expression or an equation.
Explain how to determine if a number is a solution to an equation.

Brandon Fox

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Problem 8

Identify the following as either an expression or an equation.
Explain why the equations $6 x=12$ and $x=2$ are equivalent equations.

Brandon Fox

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Problem 9

Determine whether the given number is a solution to the equation.
$$x-1=5 ; 4$$

Brandon Fox

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Problem 10

Determine whether the given number is a solution to the equation.
$$x-2=1 ;-1$$

Brandon Fox

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Problem 11

Determine whether the given number is a solution to the equation.
$$5 x=-10 ;-2$$

Brandon Fox

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Problem 12

Determine whether the given number is a solution to the equation.
$$3 x=21 ; 7$$

Brandon Fox

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Problem 13

Determine whether the given number is a solution to the equation.
$$3 x+9=3 ;-2$$

Brandon Fox

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Problem 14

Determine whether the given number is a solution to the equation.
$$2 x-1=-3 ;-1$$

Brandon Fox

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Problem 15

Solve each equation using the addition or subtraction property of equality. Be sure to check your answer.
$$x+6=5$$

Brandon Fox

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Problem 16

Solve each equation using the addition or subtraction property of equality. Be sure to check your answer.
$$x-2=10$$

Brandon Fox

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Problem 17

Solve each equation using the addition or subtraction property of equality. Be sure to check your answer.
$$q-14=6$$

Brandon Fox

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Problem 18

Solve each equation using the addition or subtraction property of equality. Be sure to check your answer.
$$w+3=-5$$

Brandon Fox

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Problem 19

Solve each equation using the addition or subtraction property of equality. Be sure to check your answer.
$$2+m=-15$$

Brandon Fox

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Problem 20

Solve each equation using the addition or subtraction property of equality. Be sure to check your answer.
$$-6+n=10$$

Brandon Fox

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Problem 21

Solve each equation using the addition or subtraction property of equality. Be sure to check your answer.
$$-23=y-7$$

Brandon Fox

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Problem 22

Solve each equation using the addition or subtraction property of equality. Be sure to check your answer.
$$-9=-21+b$$

Brandon Fox

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Problem 23

Solve each equation using the addition or subtraction property of equality. Be sure to check your answer.
$$4+c=4$$

Brandon Fox

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Problem 24

Solve each equation using the addition or subtraction property of equality. Be sure to check your answer.
$$-13+b=-13$$

Brandon Fox

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Problem 25

Solve each equation using the addition or subtraction property of equality. Be sure to check your answer.
$$4.1=2.8+a$$

Brandon Fox

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Problem 26

Solve each equation using the addition or subtraction property of equality. Be sure to check your answer.
$$5.1=-2.5+y$$

Brandon Fox

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Problem 27

Solve each equation using the addition or subtraction property of equality. Be sure to check your answer.
$$5=z-\frac{1}{2}$$

Brandon Fox

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Problem 28

Solve each equation using the addition or subtraction property of equality. Be sure to check your answer.
$$-7=p+\frac{2}{3}$$

Brandon Fox

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Problem 29

Solve each equation using the addition or subtraction property of equality. Be sure to check your answer.
$$x+\frac{5}{2}=\frac{1}{2}$$

Brandon Fox

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Problem 30

Solve each equation using the addition or subtraction property of equality. Be sure to check your answer.
$$\frac{7}{3}=x-\frac{2}{3}$$

Brandon Fox

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Problem 31

Solve each equation using the addition or subtraction property of equality. Be sure to check your answer.
$$-6.02+c=-8.15$$

Brandon Fox

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Problem 32

Solve each equation using the addition or subtraction property of equality. Be sure to check your answer.
$$p+0.035=-1.12$$

Brandon Fox

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Problem 33

Solve each equation using the addition or subtraction property of equality. Be sure to check your answer.
$$3.245+t=-0.0225$$

Brandon Fox

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Problem 34

Solve each equation using the addition or subtraction property of equality. Be sure to check your answer.
$$-1.004+k=3.0589$$

Brandon Fox

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Problem 35

Solve each equation using the multiplication or division property of equality. Be sure to check your answers.
$$6 x=54$$

Brandon Fox

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Problem 36

Solve each equation using the multiplication or division property of equality. Be sure to check your answers.
$$2 w=8$$

Brandon Fox

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Problem 37

Solve each equation using the multiplication or division property of equality. Be sure to check your answers.
$$12=-3 p$$

Brandon Fox

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Problem 38

Solve each equation using the multiplication or division property of equality. Be sure to check your answers.
$$6=-2 q$$

Brandon Fox

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Problem 39

Solve each equation using the multiplication or division property of equality. Be sure to check your answers.
$$-5 y=0$$

Brandon Fox

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Problem 40

Solve each equation using the multiplication or division property of equality. Be sure to check your answers.
$$-3 k=0$$

Brandon Fox

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Problem 41

Solve each equation using the multiplication or division property of equality. Be sure to check your answers.
$$-\frac{y}{5}=3$$

Brandon Fox

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Problem 42

Solve each equation using the multiplication or division property of equality. Be sure to check your answers.
$$-\frac{z}{7}=1$$

Brandon Fox

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Problem 43

Solve each equation using the multiplication or division property of equality. Be sure to check your answers.
$$\frac{4}{5}=-t$$

Brandon Fox

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Problem 44

Solve each equation using the multiplication or division property of equality. Be sure to check your answers.
$$-\frac{3}{7}=-h$$

Brandon Fox

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Problem 45

Solve each equation using the multiplication or division property of equality. Be sure to check your answers.
$$\frac{2}{5} a=-4$$

Brandon Fox

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Problem 46

Solve each equation using the multiplication or division property of equality. Be sure to check your answers.
$$\frac{3}{8} b=-9$$

Brandon Fox

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Problem 47

Solve each equation using the multiplication or division property of equality. Be sure to check your answers.
$$-\frac{1}{5} b=-\frac{4}{5}$$

Brandon Fox

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Problem 48

Solve each equation using the multiplication or division property of equality. Be sure to check your answers.
$$-\frac{3}{10} w=\frac{2}{5}$$

Brandon Fox

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Problem 49

Solve each equation using the multiplication or division property of equality. Be sure to check your answers.
$$-41=-x$$

Brandon Fox

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Problem 50

Solve each equation using the multiplication or division property of equality. Be sure to check your answers.
$$32=-y$$

Brandon Fox

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Problem 51

Solve each equation using the multiplication or division property of equality. Be sure to check your answers.
$$3.81=-0.03 p$$

Brandon Fox

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Problem 52

Solve each equation using the multiplication or division property of equality. Be sure to check your answers.
$$2.75=-0.5 q$$

Brandon Fox

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Problem 53

Solve each equation using the multiplication or division property of equality. Be sure to check your answers.
$$5.82 y=-15.132$$

Brandon Fox

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Problem 54

Solve each equation using the multiplication or division property of equality. Be sure to check your answers.
$$-32.3 x=-0.4522$$

Brandon Fox

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Problem 55

Write an algebraic equation to represent each English sentence. (Let $x$ represent the unknown number.) Then solve the equation.
The sum of negative eight and a number is forty-two.

Allison Knapp

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Problem 56

Write an algebraic equation to represent each English sentence. (Let $x$ represent the unknown number.) Then solve the equation.
The sum of thirty-one and a number is thirteen.

Brandon Fox

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Problem 57

Write an algebraic equation to represent each English sentence. (Let $x$ represent the unknown number.) Then solve the equation.
The difference of a number and negative six is eighteen.

Brandon Fox

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Problem 58

Write an algebraic equation to represent each English sentence. (Let $x$ represent the unknown number.) Then solve the equation.
The sum of negative twelve and a number is negative fifteen.

Brandon Fox

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Problem 59

Write an algebraic equation to represent each English sentence. (Let $x$ represent the unknown number.) Then solve the equation.
The product of a number and seven is the same as negative sixty-three.

Brandon Fox

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Problem 60

Write an algebraic equation to represent each English sentence. (Let $x$ represent the unknown number.) Then solve the equation.
The product of negative three and a number is the same as twenty-four.

Brandon Fox

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Problem 61

Write an algebraic equation to represent each English sentence. (Let $x$ represent the unknown number.) Then solve the equation.
The value 3.2 subtracted from a number is 2.1.

Brandon Fox

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Problem 62

Write an algebraic equation to represent each English sentence. (Let $x$ represent the unknown number.) Then solve the equation.
The value $-3$ subtracted from a number is 4

Brandon Fox

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Problem 63

Write an algebraic equation to represent each English sentence. (Let $x$ represent the unknown number.) Then solve the equation.
The quotient of a number and twelve is one-third.

Brandon Fox

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Problem 64

Write an algebraic equation to represent each English sentence. (Let $x$ represent the unknown number.) Then solve the equation.
Eighteen is equal to the quotient of a number and two.

Brandon Fox

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Problem 65

Write an algebraic equation to represent each English sentence. (Let $x$ represent the unknown number.) Then solve the equation.
The sum of a number and $\frac{5}{8}$ is $\frac{13}{8} .$

Brandon Fox

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Problem 66

Write an algebraic equation to represent each English sentence. (Let $x$ represent the unknown number.) Then solve the equation.
The difference of a number and $\frac{2}{3}$ is $\frac{1}{3}$

Brandon Fox

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Problem 67

Solve each equation using the appropriate property of equality.
$$a-9=1$$

Brandon Fox

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Problem 68

Solve each equation using the appropriate property of equality.
$$b-2=-4$$

Brandon Fox

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Problem 69

Solve each equation using the appropriate property of equality.
$$-9 x=1$$

Brandon Fox

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Problem 70

Solve each equation using the appropriate property of equality.
$$-2 k=-4$$

Brandon Fox

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Problem 71

Solve each equation using the appropriate property of equality.
$$-\frac{2}{3} h=8$$

Brandon Fox

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Problem 72

Solve each equation using the appropriate property of equality.
$$\frac{3}{4} p=15$$

Brandon Fox

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Problem 73

Solve each equation using the appropriate property of equality.
$$\frac{2}{3}+t=8$$

Brandon Fox

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Problem 74

Solve each equation using the appropriate property of equality.
$$\frac{3}{4}+y=15$$

Brandon Fox

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Problem 75

Solve each equation using the appropriate property of equality.
$$\frac{r}{3}=-12$$

Brandon Fox

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Problem 76

Solve each equation using the appropriate property of equality.
$$\frac{d}{-4}=5$$

Brandon Fox

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Problem 77

Solve each equation using the appropriate property of equality.
$$k+16=32$$

Brandon Fox

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Problem 78

Solve each equation using the appropriate property of equality.
$$-18=-9+t$$

Brandon Fox

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Problem 79

Solve each equation using the appropriate property of equality.
$$16 k=32$$

Brandon Fox

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Problem 80

Solve each equation using the appropriate property of equality.
$$-18=-9$$

Brandon Fox

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Problem 81

Solve each equation using the appropriate property of equality.
$$7=-4 q$$

Brandon Fox

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Problem 82

Solve each equation using the appropriate property of equality.
$$-3 s=10$$

Brandon Fox

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Problem 83

Solve each equation using the appropriate property of equality.
$$-4+q=7$$

Brandon Fox

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Problem 84

Solve each equation using the appropriate property of equality.
$$s-3=10$$

Brandon Fox

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Problem 85

Solve each equation using the appropriate property of equality.
$$-\frac{1}{3} d=12$$

Brandon Fox

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Problem 86

Solve each equation using the appropriate property of equality.
$$-\frac{2}{5} m=10$$

Brandon Fox

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Problem 87

Solve each equation using the appropriate property of equality.
$$4=\frac{1}{2}+z$$

Brandon Fox

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Problem 88

Solve each equation using the appropriate property of equality.
$$3=\frac{1}{4}+p$$

Brandon Fox

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Problem 89

Solve each equation using the appropriate property of equality.
$$1.2 y=4.8$$

Brandon Fox

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Problem 90

Solve each equation using the appropriate property of equality.
$$4.3 w=8.6$$

Brandon Fox

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Problem 91

Solve each equation using the appropriate property of equality.
$$4.8=1.2+y$$

Brandon Fox

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Problem 92

Solve each equation using the appropriate property of equality.
$$8.6=w-4.3$$

Brandon Fox

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Problem 93

Solve each equation using the appropriate property of equality.
$$0.0034=y-0.405$$

Brandon Fox

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Problem 94

Solve each equation using the appropriate property of equality.
$$-0.98=m+1.0034$$

Brandon Fox

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Problem 95

Determine if the equation is a linear equation in one variable. Answer yes or no.
$$4 p+5=0$$

Brandon Fox

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Problem 96

Determine if the equation is a linear equation in one variable. Answer yes or no.
$$3 x-5 y=0$$

Brandon Fox

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Problem 97

Determine if the equation is a linear equation in one variable. Answer yes or no.
$$4+2 a^{2}=5$$

Brandon Fox

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Problem 98

Determine if the equation is a linear equation in one variable. Answer yes or no.
$$-8 t=7$$

Brandon Fox

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Problem 99

Determine if the equation is a linear equation in one variable. Answer yes or no.
$$x-4=9$$

Brandon Fox

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Problem 100

Determine if the equation is a linear equation in one variable. Answer yes or no.
$$2 x^{3}+y=0$$

Brandon Fox

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Problem 101

Determine if the equation is a linear equation in one variable. Answer yes or no.
$$19 b=-3$$

Brandon Fox

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Problem 102

Determine if the equation is a linear equation in one variable. Answer yes or no.
$$13+x=19$$

Brandon Fox

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Problem 103

Construct an equation with the given solution set. Answers will vary.
$$\{6\}$$

Brandon Fox

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Problem 104

Construct an equation with the given solution set. Answers will vary.
$$\{-4\}$$

Brandon Fox

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Problem 105

Construct an equation with the given solution set. Answers will vary.
$$\{-4\}$$

Brandon Fox

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Problem 106

Construct an equation with the given solution set. Answers will vary.
$$\{-10\}$$

Brandon Fox

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Problem 107

Construct an equation with the given solution set. Answers will vary.
$$\{0\}$$

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Problem 108

Construct an equation with the given solution set. Answers will vary.
$$\{1\}$$

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Problem 109

Simplify by collecting the like terms. Then solve the equation.
$$5 x-4 x+7=8-2$$

Brandon Fox

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Problem 110

Simplify by collecting the like terms. Then solve the equation.
$$2+3=2 y+1-y$$

Brandon Fox

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Problem 111

Simplify by collecting the like terms. Then solve the equation.
$$6 p-3 p=15+6$$

Brandon Fox

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Problem 112

Simplify by collecting the like terms. Then solve the equation.
$$12-20=2 t+2 t$$

Brandon Fox

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