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Algebraic Expressions and Equations: 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 a−2 b+5 c6 a−2 b+5 c size 12{6a - 2b+5c} {}

Solution

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

Exercise 2

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

Exercise 3

7 m−3 n7 m−3 n size 12{7m - 3n} {}

Solution

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

Exercise 4

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

Exercise 5

x+2 n−zx+2 n−z size 12{x+2n - z} {}

Solution

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

Exercise 6

y−5y−5 size 12{y - 5} {}

Exercise 7

−y−3 z−y−3 z size 12{ - y - 3z} {}

Solution

−y−y size 12{ - y} {}, −3 z−3 z size 12{ - 3z} {}

Exercise 8

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

Exercise 9

−4−4 size 12{ - 4} {}

Solution

−4−4 size 12{ - 4} {}

Exercise 10

−6−6 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 n−5 n size 12{ - 5n} {}, how many nn size 12{n} {}’s are indicated?

Solution

-5

Exercise 16

In the expression −10y−10y 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 a−2 s5 a−2 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 n−3 r7 n−3 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 y−3 s,9 x+2 y−3 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

10a−2 b+5 c10a−2 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 s−2 t+1−5 s−2 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 m−4 n+5−3 m−4 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

m−4m−4 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 y−x+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 b−6−a+3 b−6 size 12{ - a+3b - 6} {}, if a=−3a=−3 size 12{a= - 3} {} and b=0b=0 size 12{b=0} {}

Exercise 27

5 x−4 y−7 y+y−7 x5 x−4 y−7 y+y−7 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

2a−6b−3a−a+2b2a−6b−3a−a+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

a2−6 a+4a2−6 a+4 size 12{a rSup { size 8{2} } - 6a+4} {}, if a=−2a=−2 size 12{a= - 2} {}

Solution

20

Exercise 30

m2−8 m−6m2−8 m−6 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 a2−6 a+115 a2−6 a+11 size 12{5a rSup { size 8{2} } - 6a+"11"} {}, if a=0a=0 size 12{a=0} {}

Exercise 33

−k2−k−1−k2−k−1 size 12{ - k rSup { size 8{2} } - k - 1} {}, if k=−1k=−1 size 12{k= - 1} {}

Solution

-1

Exercise 34

−h2−2 h−3−h2−2 h−3 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

a8−2 a+1a8−2 a+1 size 12{ { {a} over {8} } - 2a+1} {}, if a=24a=24 size 12{a="24"} {}

Exercise 37

5 x7+3 x−75 x7+3 x−7 size 12{ { {5x} over {7} } +3x - 7} {}, if x=14x=14 size 12{x="14"} {}

Solution

45

Exercise 38

3 k4−5 k+183 k4−5 k+18 size 12{ { {3k} over {4} } - 5k+"18"} {}, if k=16k=16 size 12{k="16"} {}

Exercise 39

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

Solution

55

Exercise 40

−7 h9−7 h−7−7 h9−7 h−7 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 y−x72 y−x 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

−a−b−a−b 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

−x−x−y−x−x−y 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)2−6(y+2)−6(y+2)2−6(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

(a−7)2−2(a−7)−2(a−7)2−2(a−7)−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+5−2 a+14 a+5−2 a+1 size 12{4a+5 - 2a+1} {}

Solution

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

Exercise 48

7 x+3 x−14x7 x+3 x−14x size 12{7x+3x - "14"x} {}

Exercise 49

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

Solution

−4 n+4 m−3−4 n+4 m−3 size 12{ - 4n+4m - 3} {}

Exercise 50

−9 k−8 h−k+6 h−9 k−8 h−k+6 h size 12{ - 9k - 8h - k+6h} {}

Exercise 51

−x+5 y−8 x−6 x+7 y−x+5 y−8 x−6 x+7 y size 12{ - x+5y - 8x - 6x+7y} {}

Solution

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

Exercise 52

6 n−2 n+6−2−n6 n−2 n+6−2−n size 12{6n - 2n+6 - 2 - n} {}

Exercise 53

0 m+3 k−5 s+2 m−s0 m+3 k−5 s+2 m−s size 12{0m+3k - 5s+2m - s} {}

Solution

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

Exercise 54

∣−8∣a+∣2∣b−∣−4∣a∣−8∣a+∣2∣b−∣−4∣a size 12{ lline - 8 rline a+ lline 2 rline b - lline - 4 rline a} {}

Exercise 55

∣6∣h−∣−7∣k+∣−12∣h+∣4∣⋅∣−5∣h∣6∣h−∣−7∣k+∣−12∣h+∣4∣⋅∣−5∣h size 12{ lline 6 rline h - lline - 7 rline k+ lline - "12" rline h+ lline 4 rline cdot lline - 5 rline h} {}

Solution

38h−7k38h−7k size 12{"38"h - 7k} {}

Exercise 56

∣0∣a−0 a+0∣0∣a−0 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

y−3=−7y−3=−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

x−4=−6x−4=−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

x−8=3x−8=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

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

Exercise 67

−3 x=9−3 x=9 size 12{ - 3x=9} {}

Solution

x=−3x=−3 size 12{x= - 3} {}

Exercise 68

−2 x=5−2 x=5 size 12{ - 2x=5} {}

Exercise 69

−5 x=−5−5 x=−5 size 12{ - 5x= - 5} {}

Solution

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

Exercise 70

−3 x=−1−3 x=−1 size 12{ - 3x= - 1} {}

Exercise 71

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

Solution

x=−27x=−27 size 12{x= - "27"} {}

Exercise 72

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

Exercise 73

−7=3 y−7=3 y size 12{ - 7=3y} {}

Solution

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

Exercise 74

−7=x3−7=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 x−13=−5 x size 12{ { { - 1} over {3} } = - 5x} {}

Solution

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

Exercise 78

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

Exercise 79

−16=s−6−16=s−6 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

x−5=−6x−5=−6 size 12{x - 5= - 6} {}

Exercise 83

−32x=6−32x=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 x−5=−3−4 x−5=−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

a−5−3=−2a−5−3=−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 2−4=63 y 2−4=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 x7−4=4−3 x7−4=4 size 12{ { { - 3x} over {7} } - 4=4} {}

Exercise 95

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

Solution

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

Exercise 96

−4 k−6=7−4 k−6=7 size 12{ - 4k - 6=7} {}

Exercise 97

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

Solution

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

Exercise 98

−6 x4=2−6 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 y−11=136 y−11=13 size 12{6y - "11"="13"} {}

Exercise 105

−3 x+8=−7−3 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

x−3=8x−3=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

w2−15=4w2−15=4 size 12{ { {w} over {2} } - "15"=4} {}

Solution

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

Exercise 110

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

Exercise 111

2 x 3−5=8 2 x 3−5=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=3−2− 2 x 7=3 size 12{ - 2 - { {2x} over {7} } =3} {}

Solution

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

Exercise 114

3−x=43−x=4 size 12{3 - x=4} {}

Exercise 115

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

Solution

y=−3y=−3 size 12{y= - 3} {}

Exercise 116

3−z=−23−z=−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 y−6=−4+3 y6 y−6=−4+3 y size 12{6y - 6= - 4+3y} {}

Solution

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

Exercise 120

3=4 a−2 a+a3=4 a−2 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 w−6=4+2 w5 w−6=4+2 w size 12{5w - 6=4+2w} {}

Exercise 123

8−3 a=32−2 a8−3 a=32−2 a size 12{8 - 3a="32" - 2a} {}

Solution

a=−24a=−24 size 12{a= - "24"} {}

Exercise 124

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

Exercise 125

x+2=3−xx+2=3−x size 12{x+2=3 - x} {}

Solution

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

Exercise 126

5 y+2 y−1=6 y5 y+2 y−1=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 3−2=16x3+ 3 x 3−2=16 size 12{ { {x} over {3} } + { {3x} over {3} } - 2="16"} {}

Exercise 131

x−2=6−xx−2=6−x size 12{x - 2=6 - x} {}

Solution

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

Exercise 132

−5 x7= 2 x 7−5 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 x4−11 3 x 4+5=−3 x4−11 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 13−4= 7 y 26+1 5 y 13−4= 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 10−2−3m5= 6 m 10−2 size 12{ { { - 3,} over {5} } = { {6m} over {"10"} } - 2} {}

Exercise 139

−3 m2+1=5 m−3 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 z5−3 z=2 z5 size 12{ - 3z= { {2z} over {5} } } {}

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