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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 ( [link] )

For problems 1-10, specify each term.

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

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

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

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

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

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

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

x size 12{x} {} , 2 n size 12{2n} {} , z size 12{ - z} {}

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y 5 size 12{y - 5} {}

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

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

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

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4 size 12{ - 4} {}

4 size 12{ - 4} {}

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

k size 12{k} {}

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

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

7

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

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

-5

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

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

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

-27

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

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

1

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

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

-5

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

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

0

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

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

5

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

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

18

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

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

20

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

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

11

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

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

-1

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

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

-93

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

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

45

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

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

55

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

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

10

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

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

-6

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

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

-14

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

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Combining like terms using addition and subtraction ( [link] )

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

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

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

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

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

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

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

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

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

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

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

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

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

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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} {}

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

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

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Equations of the form a x = b And x a = b , translating words to mathematical symbols , and solving problems ( [link] , [link] , [link] )

For problems 57-140, solve each equation.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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1 9 = k 3 size 12{ { { - 1} over {9} } = { {k} over {3} } } {}

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1 6 = s 6 size 12{ { { - 1} over {6} } = { {s} over { - 6} } } {}

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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Source:  OpenStax, Fundamentals of mathematics. OpenStax CNX. Aug 18, 2010 Download for free at http://cnx.org/content/col10615/1.4
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