Question 98601
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twice the reciprocal of a number is nine more than five times the number. 
find the number.
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A number = THE number = {{{x}}}

The reciprocal of A number or THE number = {{{1/x}}}

Replace "a number" and "the number" by x:
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twice the reciprocal of a number is nine more than five times the number. 

twice the reciprocal of {{{x}}} is nine more than five times {{{x}}}.
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Replace "the reciprocal of {{{x}}}" by {{{1/x}}}
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twice {{{1/x}}} is nine more than five times {{{x}}}.
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Replace "twice {{{1/x}}}" by {{{2/x}}}.
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{{{2/x}}} is nine more than five times {{{x}}}.
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Replace "five times {{{x}}}" by {{{5x}}}
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{{{2/x}}} is nine more than {{{5x}}}.
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Replace "nine more than {{{5x}}}" by {{{5x+9}}}
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{{{2/x}}} is {{{5x+9}}}.
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Replace "is by " = "
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{{{2/x}}} = {{{5x+9}}}.
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Multiply through by x
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{{{2}}} = {{{5x^2+9x}}}
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Get 0 on the left:
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{{{0}}} = {{{5x^2+9x-2}}}

{{{0}}} = {{{(5x-1)(x+2)}}}

{{{5x-1=0}}}, {{{x+2=0}}}
{{{5x=1}}},   {{{x=-2}}}
{{{x=1/5}}}, {{{x=-2}}}
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Two solutions: {{{1/5}}}, {{{-2}}}

Edwin</pre>