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Nine from some number is four.

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

Five less than some quantity is eight.

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

Exercises

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

A quantity less twelve.

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

Six more than an unknown number.

A number minus four.

x 4 size 12{x - 4} {}

A number plus seven.

A number increased by one.

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

A number decreased by ten.

Negative seven added to some number.

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

Negative nine added to a number.

A number plus the opposite of six.

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

A number minus the opposite of five.

A number minus the opposite of negative one.

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

A number minus the opposite of negative twelve.

Eleven added to three times a number.

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

Six plus five times an unknown number.

Twice a number minus seven equals four.

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

Ten times a quantity increased by two is nine.

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

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

Four times a number minus twenty-nine is eleven.

Three fifths of a number plus eight is fifty.

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

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

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} {}

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

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"} {}

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

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} {}

A number is equal to itself minus three times itself.

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

x 7 + 2 = 17

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

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

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

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

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

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

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

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} {}

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

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} {}

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

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} {}

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.

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} {}

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.

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} } } {}

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

( [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} } } {}

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

( [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, Algebra i for the community college. OpenStax CNX. Dec 19, 2014 Download for free at http://legacy.cnx.org/content/col11598/1.3
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