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Nine from some number is four.

x 9 = 4 size 12{x - 9=4} {}

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Five less than some quantity is eight.

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

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Exercises

Translate each phrase or sentence to a mathematical expression or equation.

A quantity less twelve.

x 12 size 12{x - "12"} {}

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Six more than an unknown number.

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A number minus four.

x 4 size 12{x - 4} {}

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A number increased by one.

x + 1 size 12{x+1} {}

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A number decreased by ten.

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Negative seven added to some number.

7 + x size 12{ - 7+x} {}

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Negative nine added to a number.

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A number plus the opposite of six.

x + 6 size 12{x+ left ( - 6 right )} {}

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A number minus the opposite of five.

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A number minus the opposite of negative one.

x 1 size 12{x - left [ - left ( - 1 right ) right ]} {}

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A number minus the opposite of negative twelve.

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Eleven added to three times a number.

3 x + 11 size 12{3x+"11"} {}

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Six plus five times an unknown number.

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Twice a number minus seven equals four.

2 x 7 = 4 size 12{2x - 7=4} {}

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Ten times a quantity increased by two is nine.

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When fourteen is added to two times a number the result is six.

14 + 2 x = 6 size 12{"14"+2x=6} {}

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Four times a number minus twenty-nine is eleven.

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Three fifths of a number plus eight is fifty.

3 5 x + 8 = 50 size 12{ { {3} over {5} } x+8="50"} {}

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Two ninths of a number plus one fifth is forty-one.

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When four thirds of a number is increased by twelve, the result is five.

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

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When seven times a number is decreased by two times the number, the result is negative one.

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When eight times a number is increased by five, the result is equal to the original number plus twenty-six.

8 x + 5 = x + 26 size 12{8x+5=x+"26"} {}

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Five more than some number is three more than four times the number.

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When a number divided by six is increased by nine, the result is one.

x 6 + 9 = 1 size 12{ { {x} over {6} } +9=1} {}

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A number is equal to itself minus three times itself.

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A number divided by seven, plus two, is seven­teen.

x 7 + 2 = 17

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A number divided by nine, minus five times the number, is equal to one more than the number.

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When two is subtracted from some number, the result is ten.

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

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When four is subtracted from some number, the result is thirty-one.

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Three less than some number is equal to twice the number minus six.

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

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Thirteen less than some number is equal to three times the number added to eight.

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When twelve is subtracted from five times some number, the result is two less than the original number.

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

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When one is subtracted from three times a num­ber, the result is eight less than six times the original number.

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When a number is subtracted from six, the result is four more than the original number.

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

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When a number is subtracted from twenty-four, the result is six less than twice the number.

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A number is subtracted from nine. This result is then increased by one. The result is eight more than three times the number.

9 x + 1 = 3 x + 8 size 12{9 - x+1=3x+8} {}

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Five times a number is increased by two. This result is then decreased by three times the num­ber. The result is three more than three times the number.

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Twice a number is decreased by seven. This re­sult is decreased by four times the number. The result is negative the original number, minus six.

2 x 7 4 x = x 6 size 12{2x - 7 - 4x= - x - 6} {}

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Fifteen times a number is decreased by fifteen. This result is then increased by two times the number. The result is negative five times the original number minus the opposite of ten.

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Exercises for review

( [link] ) 8 9 size 12{ { {8} over {9} } } {} of what number is 2 3 size 12{ { {2} over {3} } } {} ?

3 4 size 12{ { {3} over {4} } } {}

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( [link] ) Find the value of 21 40 + 17 30 size 12{ { {"21"} over {"40"} } + { {"17"} over {"30"} } } {} .

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( [link] ) Find the value of 3 1 12 + 4 1 3 + 1 1 4 size 12{3 { {1} over {"12"} } +4 { {1} over {3} } +1 { {1} over {4} } } {} .

8 2 3 size 12{8 { {2} over {3} } } {}

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( [link] ) Convert 6 . 11 1 5 size 12{6 "." "11" { {1} over {5} } } {} to a fraction.

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( [link] ) Solve the equation 3 x 4 + 1 = 5 size 12{ { {3x} over {4} } +1= - 5} {} .

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

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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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