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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.

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117.
After 24 years I shall be 3 times as old as I was 4 years ago. Find my present age.

Let my present age be x years.

∴ After 24 years, my age will be (x + 24) years.

   4 years ago, my age was (x - 4) years.

   According to the given condition, we have

                          (x + 24) = 3(x - 4)

$rightwards double arrow$                         x + 24 = 3x - 12

$rightwards double arrow$                         x - 3x = - 12 - 24

$rightwards double arrow$                             -2x = -36

$rightwards double arrow$                               $space space space straight x equals fraction numerator negative 36 over denominator negative 2 end fraction equals 18$

   Thus, my present age is 18 years.