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Exercise Supplement

Module by: Wade Ellis, Denny Burzynski. E-mail the authorsEdited By: Math Editors

Summary: This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module is an exercise supplement for the chapter "Algebraic Expressions and Equations" and contains many exercise problems. Odd problems are accompanied by solutions.

Exercise Supplement

Algebraic Expressions ((Reference))

For problems 1-10, specify each term.

Exercise 1

6 a2 b+5 c6 a2 b+5 c size 12{6a - 2b+5c} {}

Solution

6 a6 a size 12{6a} {}, 2 b2 b size 12{ - 2b} {}, 5 c5 c size 12{5c} {}

Exercise 2

9 x6 y+19 x6 y+1 size 12{9x - 6y+1} {}

Exercise 3

7 m3 n7 m3 n size 12{7m - 3n} {}

Solution

7 m7 m size 12{7m} {}, 3 n3 n size 12{ - 3n} {}

Exercise 4

5 h+2 k8+4 m5 h+2 k8+4 m size 12{ - 5h+2k - 8+4m} {}

Exercise 5

x+2 nzx+2 nz size 12{x+2n - z} {}

Solution

xx size 12{x} {}, 2 n2 n size 12{2n} {}, zz size 12{ - z} {}

Exercise 6

y5y5 size 12{y - 5} {}

Exercise 7

y3 zy3 z size 12{ - y - 3z} {}

Solution

yy size 12{ - y} {}, 3 z3 z size 12{ - 3z} {}

Exercise 8

abc1abc1 size 12{ - a - b - c - 1} {}

Exercise 9

44 size 12{ - 4} {}

Solution

44 size 12{ - 4} {}

Exercise 10

66 size 12{ - 6} {}

Exercise 11

Write 1 k1 k size 12{1k} {} in a simpler way.

Solution

kk size 12{k} {}

Exercise 12

Write 1 x1 x size 12{1x} {} in a simpler way.

Exercise 13

In the expression 7 r7 r size 12{7r} {}, how many rr size 12{r} {}’s are indicated?

Solution

7

Exercise 14

In the expression 12m12m size 12{"12"m} {}, how many mm size 12{m} {}’s are indicated?

Exercise 15

In the expression 5 n5 n size 12{ - 5n} {}, how many nn size 12{n} {}’s are indicated?

Solution

-5

Exercise 16

In the expression 10y10y size 12{ - "10"y} {}, how many yy size 12{y} {}’s are indicated?

For problems 17-46, find the value of each expression.

Exercise 17

5 a2 s5 a2 s size 12{5a - 2s} {}, if a=5a=5 size 12{a= - 5} {} and s=1s=1 size 12{s=1} {}

Solution

-27

Exercise 18

7 n3 r7 n3 r size 12{7n - 3r} {}, if n=6n=6 size 12{n= - 6} {} and r=2r=2 size 12{r=2} {}

Exercise 19

9 x+2 y3 s,9 x+2 y3 s, size 12{9x+2y - 3s,} {} if x=2x=2 size 12{x= - 2} {}, y=5y=5 size 12{y=5} {}, and s=3s=3 size 12{s= - 3} {}

Solution

1

Exercise 20

10a2 b+5 c10a2 b+5 c size 12{"10"a - 2b+5c} {}, if a=0a=0 size 12{a=0} {}, b=6b=6 size 12{b= - 6} {}, and c=8c=8 size 12{c=8} {}

Exercise 21

5 s2 t+15 s2 t+1 size 12{ - 5s - 2t+1} {}, if s=2s=2 size 12{s=2} {} and t=2t=2 size 12{t= - 2} {}

Solution

-5

Exercise 22

3 m4 n+53 m4 n+5 size 12{ - 3m - 4n+5} {}, if m=1m=1 size 12{m= - 1} {} and n=1n=1 size 12{n= - 1} {}

Exercise 23

m4m4 size 12{m - 4} {}, if m=4m=4 size 12{m=4} {}

Solution

0

Exercise 24

n=2n=2 size 12{n=2} {}, if n=2n=2 size 12{n=2} {}

Exercise 25

x+2 yx+2 y size 12{ - x+2y} {}, if x=7x=7 size 12{x= - 7} {} and y=1y=1 size 12{y= - 1} {}

Solution

5

Exercise 26

a+3 b6a+3 b6 size 12{ - a+3b - 6} {}, if a=3a=3 size 12{a= - 3} {} and b=0b=0 size 12{b=0} {}

Exercise 27

5 x4 y7 y+y7 x5 x4 y7 y+y7 x size 12{5x - 4y - 7y+y - 7x} {}, if x=1x=1 size 12{x=1} {} and y=2y=2 size 12{y= - 2} {}

Solution

18

Exercise 28

2a6b3aa+2b2a6b3aa+2b size 12{2a - 6b - 3a - a+2b} {}, if a=4a=4 size 12{a=4} {} and b=-2b=-2 size 12{b=-2} {}

Exercise 29

a26 a+4a26 a+4 size 12{a rSup { size 8{2} } - 6a+4} {}, if a=2a=2 size 12{a= - 2} {}

Solution

20

Exercise 30

m28 m6m28 m6 size 12{m rSup { size 8{2} } - 8m - 6} {}, if m=5m=5 size 12{m= - 5} {}

Exercise 31

4 y2+3 y+14 y2+3 y+1 size 12{4y rSup { size 8{2} } +3y+1} {}, if y=2y=2 size 12{y= - 2} {}

Solution

11

Exercise 32

5 a26 a+115 a26 a+11 size 12{5a rSup { size 8{2} } - 6a+"11"} {}, if a=0a=0 size 12{a=0} {}

Exercise 33

k2k1k2k1 size 12{ - k rSup { size 8{2} } - k - 1} {}, if k=1k=1 size 12{k= - 1} {}

Solution

-1

Exercise 34

h22 h3h22 h3 size 12{ - h rSup { size 8{2} } - 2h - 3} {}, if h=4h=4 size 12{h= - 4} {}

Exercise 35

m6+5 mm6+5 m size 12{ { {m} over {6} } +5m} {}, if m=18m=18 size 12{m= - "18"} {}

Solution

-93

Exercise 36

a82 a+1a82 a+1 size 12{ { {a} over {8} } - 2a+1} {}, if a=24a=24 size 12{a="24"} {}

Exercise 37

5 x7+3 x75 x7+3 x7 size 12{ { {5x} over {7} } +3x - 7} {}, if x=14x=14 size 12{x="14"} {}

Solution

45

Exercise 38

3 k45 k+183 k45 k+18 size 12{ { {3k} over {4} } - 5k+"18"} {}, if k=16k=16 size 12{k="16"} {}

Exercise 39

6 a5+3 a+106 a5+3 a+10 size 12{ { { - 6a} over {5} } +3a+"10"} {}, if a=25a=25 size 12{a="25"} {}

Solution

55

Exercise 40

7 h97 h77 h97 h7 size 12{ { { - 7h} over {9} } - 7h - 7} {}, if h=18h=18 size 12{h= - "18"} {}

Exercise 41

53 a+4 b53 a+4 b size 12{5 left (3a+4b right )} {}, if a=2a=2 size 12{a= - 2} {} and b=2b=2 size 12{b=2} {}

Solution

10

Exercise 42

72 yx72 yx size 12{7 left (2y - x right )} {}, if x=1x=1 size 12{x= - 1} {} and y=2y=2 size 12{y=2} {}

Exercise 43

abab size 12{ - left (a - b right )} {}, if a=0a=0 size 12{a=0} {} and b=6b=6 size 12{b= - 6} {}

Solution

-6

Exercise 44

xxyxxy size 12{ - left (x - x - y right )} {}, if x=4x=4 size 12{x=4} {} and y=4y=4 size 12{y= - 4} {}

Exercise 45

(y+2)26(y+2)6(y+2)26(y+2)6 size 12{ \( y+2 \) rSup { size 8{2} } - 6 \( y+2 \) - 6} {}, if y=2y=2 size 12{y=2} {}

Solution

-14

Exercise 46

(a7)22(a7)2(a7)22(a7)2 size 12{ \( a - 7 \) rSup { size 8{2} } - 2 \( a - 7 \) - 2} {}, if a=7a=7 size 12{a=7} {}

Combining Like Terms Using Addition and Subtraction ((Reference))

For problems 47-56, simplify each expression by combining like terms.

Exercise 47

4 a+52 a+14 a+52 a+1 size 12{4a+5 - 2a+1} {}

Solution

2 a+62 a+6 size 12{2a+6} {}

Exercise 48

7 x+3 x14x7 x+3 x14x size 12{7x+3x - "14"x} {}

Exercise 49

7 b+4 m3+3 n7 b+4 m3+3 n size 12{ - 7b+4m - 3+3n} {}

Solution

4 n+4 m34 n+4 m3 size 12{ - 4n+4m - 3} {}

Exercise 50

9 k8 hk+6 h9 k8 hk+6 h size 12{ - 9k - 8h - k+6h} {}

Exercise 51

x+5 y8 x6 x+7 yx+5 y8 x6 x+7 y size 12{ - x+5y - 8x - 6x+7y} {}

Solution

15x+12y15x+12y size 12{ - "15"x+"12"y} {}

Exercise 52

6 n2 n+62n6 n2 n+62n size 12{6n - 2n+6 - 2 - n} {}

Exercise 53

0 m+3 k5 s+2 ms0 m+3 k5 s+2 ms size 12{0m+3k - 5s+2m - s} {}

Solution

3 k+2 m-6s3 k+2 m-6s size 12{3k+2m} {}

Exercise 54

8a+2b4a8a+2b4a size 12{ lline - 8 rline a+ lline 2 rline b - lline - 4 rline a} {}

Exercise 55

6h7k+12h+45h6h7k+12h+45h size 12{ lline 6 rline h - lline - 7 rline k+ lline - "12" rline h+ lline 4 rline cdot lline - 5 rline h} {}

Solution

38h7k38h7k size 12{"38"h - 7k} {}

Exercise 56

0a0 a+00a0 a+0 size 12{ lline 0 rline a - 0a+0} {}

Equations of the Form ax=bax=b and xa=bxa=b, Translating Words to Mathematical Symbols , and Solving Problems ((Reference),(Reference),(Reference))

For problems 57-140, solve each equation.

Exercise 57

x+1=5x+1=5 size 12{x+1=5} {}

Solution

x=4x=4 size 12{x=4} {}

Exercise 58

y3=7y3=7 size 12{y - 3= - 7} {}

Exercise 59

x+12=10x+12=10 size 12{x+"12"="10"} {}

Solution

x=2x=2 size 12{x= - 2} {}

Exercise 60

x4=6x4=6 size 12{x - 4= - 6} {}

Exercise 61

5 x=255 x=25 size 12{5x="25"} {}

Solution

x=5x=5 size 12{x=5} {}

Exercise 62

3 x=173 x=17 size 12{3x="17"} {}

Exercise 63

x2=6x2=6 size 12{ { {x} over {2} } =6} {}

Solution

x=12x=12 size 12{x="12"} {}

Exercise 64

x8=3x8=3 size 12{ { {x} over { - 8} } =3} {}

Exercise 65

x15=1x15=1 size 12{ { {x} over {"15"} } = - 1} {}

Solution

x=15x=15 size 12{x= - "15"} {}

Exercise 66

x4=3x4=3 size 12{ { {x} over { - 4} } = - 3} {}

Exercise 67

3 x=93 x=9 size 12{ - 3x=9} {}

Solution

x=3x=3 size 12{x= - 3} {}

Exercise 68

2 x=52 x=5 size 12{ - 2x=5} {}

Exercise 69

5 x=55 x=5 size 12{ - 5x= - 5} {}

Solution

x=1x=1 size 12{x=1} {}

Exercise 70

3 x=13 x=1 size 12{ - 3x= - 1} {}

Exercise 71

x3=9x3=9 size 12{ { {x} over { - 3} } =9} {}

Solution

x=27x=27 size 12{x= - "27"} {}

Exercise 72

a5=2a5=2 size 12{ { {a} over { - 5} } =2} {}

Exercise 73

7=3 y7=3 y size 12{ - 7=3y} {}

Solution

y=73y=73 size 12{y= - { {7} over {3} } } {}

Exercise 74

7=x37=x3 size 12{ - 7= { {x} over {3} } } {}

Exercise 75

m4=25m4=25 size 12{ { {m} over {4} } = { { - 2} over {5} } } {}

Solution

m=85m=85 size 12{m= - { {8} over {5} } } {}

Exercise 76

4 y=124 y=12 size 12{4y= { {1} over {2} } } {}

Exercise 77

13=5 x13=5 x size 12{ { { - 1} over {3} } = - 5x} {}

Solution

x=115x=115 size 12{x= { {1} over {"15"} } } {}

Exercise 78

19=k319=k3 size 12{ { { - 1} over {9} } = { {k} over {3} } } {}

Exercise 79

16=s616=s6 size 12{ { { - 1} over {6} } = { {s} over { - 6} } } {}

Solution

s=1s=1 size 12{s=1} {}

Exercise 80

04=4 s04=4 s size 12{ { {0} over {4} } =4s} {}

Exercise 81

x+2=1x+2=1 size 12{x+2= - 1} {}

Solution

x=3x=3 size 12{x= - 3} {}

Exercise 82

x5=6x5=6 size 12{x - 5= - 6} {}

Exercise 83

32x=632x=6 size 12{ { { - 3} over {2} } x=6} {}

Solution

x=4x=4 size 12{x= - 4} {}

Exercise 84

3 x+2=73 x+2=7 size 12{3x+2=7} {}

Exercise 85

4 x5=34 x5=3 size 12{ - 4x - 5= - 3} {}

Solution

x=-12x=-12 size 12{x= { {1} over {2} } } {}

Exercise 86

x6+1=4x6+1=4 size 12{ { {x} over {6} } +1=4} {}

Exercise 87

a53=2a53=2 size 12{ { {a} over { - 5} } - 3= - 2} {}

Solution

a=5a=5 size 12{a= - 5} {}

Exercise 88

4 x3=7 4 x3=7 size 12{ { {4x} over {3} } =7} {}

Exercise 89

2 x 5+2=82 x 5+2=8 size 12{ { {2x} over {5} } +2=8} {}

Solution

x=15x=15 size 12{x="15"} {}

Exercise 90

3 y 24=63 y 24=6 size 12{ { {3y} over {2} } - 4=6} {}

Exercise 91

m+3=8m+3=8 size 12{m+3=8} {}

Solution

x=5x=5 size 12{x=5} {}

Exercise 92

1 x 2=2 1 x 2=2 size 12{ { {1x} over {2} } =2} {}

Exercise 93

2 a 3=5 2 a 3=5 size 12{ { {2a} over {3} } =5} {}

Solution

a=152a=152 size 12{a= { {"15"} over {2} } } {}

Exercise 94

3 x74=43 x74=4 size 12{ { { - 3x} over {7} } - 4=4} {}

Exercise 95

5 x26=10 5 x26=10 size 12{ { {5x} over { - 2} } - 6= - "10"} {}

Solution

x=85x=85 size 12{x= { {8} over {5} } } {}

Exercise 96

4 k6=74 k6=7 size 12{ - 4k - 6=7} {}

Exercise 97

3 x2+1=43 x2+1=4 size 12{ { { - 3x} over { - 2} } +1=4} {}

Solution

x =2 x =2 size 12{x=2} {}

Exercise 98

6 x4=26 x4=2 size 12{ { { - 6x} over {4} } =2} {}

Exercise 99

x+9=14x+9=14 size 12{x+9="14"} {}

Solution

x=5x=5 size 12{x=5} {}

Exercise 100

y+5=21y+5=21 size 12{y+5="21"} {}

Exercise 101

y+5=7y+5=7 size 12{y+5= - 7} {}

Solution

y=12y=12 size 12{y= - "12"} {}

Exercise 102

4 x=244 x=24 size 12{4x="24"} {}

Exercise 103

4 w =374 w =37 size 12{4w="37"} {}

Solution

w=374w=374 size 12{w= { {"37"} over {4} } } {}

Exercise 104

6 y11=136 y11=13 size 12{6y - "11"="13"} {}

Exercise 105

3 x+8=73 x+8=7 size 12{ - 3x+8= - 7} {}

Solution

x=5x=5 size 12{x=5} {}

Exercise 106

3 z+9=513 z+9=51 size 12{3x+9= - "51"} {}

Exercise 107

x3=8x3=8 size 12{ { {x} over { - 3} } =8} {}

Solution

x=24x=24 size 12{x= - "24"} {}

Exercise 108

6 y 7=5 6 y 7=5 size 12{ { {6y} over {7} } =5} {}

Exercise 109

w215=4w215=4 size 12{ { {w} over {2} } - "15"=4} {}

Solution

w=38w=38 size 12{w="38"} {}

Exercise 110

x223=10x223=10 size 12{ { {x} over { - 2} } - "23"= - "10"} {}

Exercise 111

2 x 35=8 2 x 35=8 size 12{ { {2x} over {3} } - 5=8} {}

Solution

x=392x=392 size 12{x= { {"39"} over {2} } } {}

Exercise 112

3 z 4=78 3 z 4=78 size 12{ { {3z} over {4} } = { { - 7} over {8} } } {}

Exercise 113

2 2 x 7=32 2 x 7=3 size 12{ - 2 - { {2x} over {7} } =3} {}

Solution

x=352x=352 size 12{x= - { {"35"} over {2} } } {}

Exercise 114

3x=43x=4 size 12{3 - x=4} {}

Exercise 115

5y=25y=2 size 12{ - 5 - y= - 2} {}

Solution

y=3y=3 size 12{y= - 3} {}

Exercise 116

3z=23z=2 size 12{3 - z= - 2} {}

Exercise 117

3 x+2 x=63 x+2 x=6 size 12{3x+2x=6} {}

Solution

x=65x=65 size 12{x= { {6} over {5} } } {}

Exercise 118

4 x+1+6 x=104 x+1+6 x=10 size 12{4x+1+6x="10"} {}

Exercise 119

6 y6=4+3 y6 y6=4+3 y size 12{6y - 6= - 4+3y} {}

Solution

y=23y=23 size 12{y= { {2} over {3} } } {}

Exercise 120

3=4 a2 a+a3=4 a2 a+a size 12{3=4a - 2a+a} {}

Exercise 121

3 m+4=2 m+13 m+4=2 m+1 size 12{3m+4=2m+1} {}

Solution

m=3m=3 size 12{m= - 3} {}

Exercise 122

5 w6=4+2 w5 w6=4+2 w size 12{5w - 6=4+2w} {}

Exercise 123

83 a=322 a83 a=322 a size 12{8 - 3a="32" - 2a} {}

Solution

a=24a=24 size 12{a= - "24"} {}

Exercise 124

5 x2 x+6 x=135 x2 x+6 x=13 size 12{5x - 2x+6x="13"} {}

Exercise 125

x+2=3xx+2=3x size 12{x+2=3 - x} {}

Solution

x=12x=12 size 12{x= { {1} over {2} } } {}

Exercise 126

5 y+2 y1=6 y5 y+2 y1=6 y size 12{5y+2y - 1=6y} {}

Exercise 127

x=32x=32 size 12{x="32"} {}

Solution

x=32x=32 size 12{x="32"} {}

Exercise 128

k=4k=4 size 12{k= - 4} {}

Exercise 129

3 x 2+4= 5 x2=6 3 x 2+4= 5 x2=6 size 12{ { {3x} over {2} } +4= { {5x} over {2} } =6} {}

Solution

x=2x=2 size 12{x= - 2} {}

Exercise 130

x3+ 3 x 32=16x3+ 3 x 32=16 size 12{ { {x} over {3} } + { {3x} over {3} } - 2="16"} {}

Exercise 131

x2=6xx2=6x size 12{x - 2=6 - x} {}

Solution

x=4x=4 size 12{x=4} {}

Exercise 132

5 x7= 2 x 75 x7= 2 x 7 size 12{ { { - 5x} over {7} } = { {2x} over {7} } } {}

Exercise 133

2x3+1=52x3+1=5 size 12{ { {2x} over {3} } +1=5} {}

Solution

x=6x=6 size 12{x=6} {}

Exercise 134

3 x5+3= 2 x 5+2 3 x5+3= 2 x 5+2 size 12{ { { - 3x} over {5} } +3= { {2x} over {5} } +2} {}

Exercise 135

3 x 4+5=3 x411 3 x 4+5=3 x411 size 12{ { {3x} over {4} } +5= { { - 3x} over {4} } - "11"} {}

Solution

x=323x=323 size 12{x= { { - "32"} over {3} } } {}

Exercise 136

3 x 7=3 x7+123 x 7=3 x7+12 size 12{ { {3x} over {7} } = { { - 3x} over {7} } +"12"} {}

Exercise 137

5 y 134= 7 y 26+1 5 y 134= 7 y 26+1 size 12{ { {5y} over {"13"} } - 4= { {7y} over {"26"} } +1} {}

Solution

y=1303y=1303 size 12{y= { {"130"} over {3} } } {}

Exercise 138

3m5= 6 m 1023m5= 6 m 102 size 12{ { { - 3,} over {5} } = { {6m} over {"10"} } - 2} {}

Exercise 139

3 m2+1=5 m3 m2+1=5 m size 12{ { { - 3m} over {2} } +1=5m} {}

Solution

m=213m=213 size 12{m= { {2} over {"13"} } } {}

Exercise 140

3 z=2 z53 z=2 z5 size 12{ - 3z= { {2z} over {5} } } {}

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Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks

Module to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks