Beginning and Intermediate Algebra

Margaret L. Lial, John Hornsby, Terry McGinnis

Chapter 2

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

Educators

Section 1

The Addition Property of Equality

Problem 1

Complete each statement with the correct response. The following terms may be used once, more than once, or not at all.
$\begin{array}{lll}\text { linear } & \text { expression } & \text { solution set } & \text { multiplication }\end{array}$
equation addition $\quad$ equivalent equations $\quad$ variable
$\mathrm{A}(\mathrm{n})$ ________________ includes an equality symbol, while a(n) ______________ does not.

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Problem 2

$\mathrm{A}(\mathrm{n})$ _____________ equation in one ______________ (here $x$ ) is an equation that can be written in the form $a x+b(=I \neq) 0$.

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Problem 3

Equations that have exactly the same solution set are ________________

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Problem 4

The ________________ property of equality states that the same expression may be added to or subtracted from each side of an equation without changing the ________________

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Problem 5

Decide whether each of the following is an expression or an equation. If it is an expression, simplify it. If it is an equation, solve it.
(a) $5 x+8-4 x+7$
(b) $-6 z+12+7 z-5$
(c) $5 x+8-4 x=7$
(d) $-6 z+12+7 z=-5$

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Problem 6

Which pairs of equations are equivalent equations?
A. $x+2=6$ and $x=4$
B. $10-x=5$ and $x=-5$
C. $x+3=9$ and $x=6$
D. $4+x=8$ and $x=-4$

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Problem 7

Which of the following are not linear equations in one variable?
A. $x^{2}-5 x+6=0$
B. $4 x+3 y=12$
C. $3 x-4=0$
D. $7 x-6 x=3+9 x$

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Problem 8

Explain how to check a solution of an equation.

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Problem 9

Solve each equation, and check the solution.
$x-3=9$

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Problem 10

$x-9=8$

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Problem 11

$x-12=19$

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Problem 12

$x-18=22$

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Problem 13

$x-6=-9$

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Problem 14

$x-5=-7$

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Problem 15

$r+8=12$

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Problem 16

$x+7=11$

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Problem 17

$x+26=17$

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Problem 18

$x+47=26$

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Problem 19

$x-8.4=-2.1$

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Problem 20

$x-15.5=-5.1$

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Problem 21

$t+12.3=-4.6$

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Problem 22

$x+21.5=-13.4$

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Problem 23

$x+\frac{1}{4}=-\frac{1}{2}$

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Problem 24

$x+\frac{2}{3}=-\frac{1}{6}$

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Problem 25

$k-\frac{3}{4}=-\frac{2}{3}$

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Problem 26

$p-\frac{5}{9}=-\frac{1}{2}$

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Problem 27

$7+r=-3$

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Problem 28

$8+k=-4$

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Problem 29

$2=p+15$

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Problem 30

$5=z+19$

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Problem 31

$-4=x-14$

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Problem 32

$-7=x-22$

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Problem 33

$5.2=z-4.9$

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Problem 34

$11.8=z-3.6$

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Problem 35

$-\frac{1}{3}=x-\frac{3}{5}$

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Problem 36

$-\frac{1}{4}=x-\frac{2}{3}$

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Problem 37

$8 x-3=9 x$

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Problem 38

$6 x-4=7 x$

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Problem 39

$6 t-2=5 t$

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Problem 40

$4 z-6=3 z$

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Problem 41

$3 x=2 x+7$

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Problem 42

$5 x=4 x+9$

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Problem 43

$10 x+4=9 x$

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Problem 44

$8 t+5=7 t$

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Problem 45

$\frac{2}{5} w-6=\frac{7}{5} w$

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Problem 46

$\frac{2}{7} z-2=\frac{9}{7} z$

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Problem 48

$\frac{1}{5} x+7=-\frac{4}{5} x$

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Problem 49

$5.6 x+2=4.6 x$

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Problem 50

$9.1 x+5=8.1 x$

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Problem 51

$1.4 x-3=0.4 x$

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Problem 52

$1.9 t-6=0.9 t$

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Problem 53

$3 x+7=2 x+4$

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Problem 54

$9 x+5=8 x+4$

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Problem 55

$8 t+6=7 t+6$

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Problem 56

$13 t+9=12 t+9$

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Problem 57

$7-4 x=-5 x+9$

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Problem 58

$3-6 x=-7 x+10$

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Problem 59

$5-x=-2 x-11$

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Problem 60

$3-8 x=-9 x-1$

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Problem 61

$1.2 y-4=0.2 y-4$

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Problem 62

$7.7 r-6=6.7 r-6$

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Problem 63

Solve each equation, and check the solution.
$4 x-6-3 x=3$

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Problem 64

$7 x-8-6 x=4$

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Problem 65

$3 x+7-2 x=0$

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Problem 66

$5 x+4-4 x=0$

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Problem 67

$3 x+6-10=2 x-2$

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Problem 68

$8 x+4-8=7 x-1$

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Problem 69

$5 t+3+2 t-6 t=4+12$

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Problem 70

$4 x-6+3 x-6 x=3+10$

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Problem 71

$6 x+5+7 x+3=12 x+4$

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Problem 72

$4 x+3+8 x+1=11 x+2$

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Problem 73

$10 x+5 x+7-4=12 x+3+2 x$

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Problem 74

$7 p+4 p+13-7=7 p+6+3 p$

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Problem 75

$5.2 q-4.6-7.1 q=-0.9 q-4.6$

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Problem 76

$4.0 x+2.7-9.6 x=-4.6 x+2.7$

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Problem 77

$\frac{5}{7} x+\frac{1}{3}=\frac{2}{5}-\frac{2}{7} x+\frac{2}{5}$

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Problem 78

$\frac{6}{7} s-\frac{3}{4}=\frac{4}{5}-\frac{1}{7} s+\frac{1}{6}$

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Problem 79

$5(3 x-2)-14 x=3$

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Problem 80

$2(3 x-4)-5 x=7$

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Problem 81

$13 p+3(2-4 p)=4$

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Problem 82

$21 w+4(6-5 w)=8$

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Problem 83

$(5 y+6)-(3+4 y)=10$

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Problem 84

$(8 r+3)-(1+7 r)=6$

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Problem 85

$2(p+5)-(9+p)=-3$

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Problem 86

$4(k+6)-(8+3 k)=-5$

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Problem 87

$-6(2 b+1)+(13 b-7)=0$

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Problem 88

$-5(3 w-3)+(16 w+1)=0$

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Problem 89

$10(-2 x+1)=-19(x+1)$

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Problem 90

$2(-3 r+2)=-5(r-3)$

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Problem 91

Solve each equation, and check the solution.
$-2(8 p+2)-3(2-7 p)-2(4+2 p)=0$

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Problem 92

$-5(1-2 z)+4(3-z)-7(3+z)=0$

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Problem 93

$4(7 x-1)+3(2-5 x)-4(3 x+5)=-6$

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Problem 94

$9(2 m-3)-4(5+3 m)-5(4+m)=-3$

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Problem 95

Work each problem.
Write an equation that requires the use of the addition property of equality, where 6 must be added to each side and the solution is a negative number.

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Problem 96

Write an equation that requires the use of the addition property of equality, where $\frac{1}{2}$ must be subtracted from each side and the solution is a positive number.

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