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Linear Equations in One Variable

Short Answer Type

111.

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112.

Solve for $straight x colon fraction numerator 7 straight x plus 14 over denominator 3 end fraction minus fraction numerator 17 minus 3 straight x over denominator 5 end fraction equals 6 straight x minus fraction numerator 4 straight x plus 2 over denominator 3 end fraction minus 5$

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113.

Solve for $space space space space straight x colon fraction numerator straight x minus left parenthesis 7 minus 8 straight x right parenthesis over denominator 9 straight x minus left parenthesis 3 plus 4 straight x right parenthesis end fraction equals 2 over 3$

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114.

Solve for $straight x colon fraction numerator left parenthesis 2 plus straight x right parenthesis left parenthesis 7 minus straight x right parenthesis over denominator left parenthesis 5 minus straight x right parenthesis left parenthesis 4 plus straight x right parenthesis end fraction equals 1$

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115.

A number is such that it is as much greater than 65 as it is less than 91. Find the number.

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116.
The numerator of a fraction is 2 less than the denominator. If 1 is added to its denominator, it becomes ½. Find the fraction.

Let the denominator of the fraction be x.

∴ Numerator = x - 2

∴           The fraction = $fraction numerator straight x minus 2 over denominator straight x end fraction$

    Since, it becomes $1 half$ when 1 is added to its denominator

i.e.             $fraction numerator straight x minus 2 over denominator straight x plus 1 end fraction equals 1 half$

   By cross multiplication, we have

                     2(x - 2) = x + 1

$rightwards double arrow$                    2x - 4 = x + 1

$rightwards double arrow$                   2x - x = 1 + 4

$rightwards double arrow$                            x = 5