document.write( "Question 134556: the additve inverse of a number divided by twelve is the same as one less than three times its reciprocal. \n" ); document.write( "

Algebra.Com's Answer #98440 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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the additive inverse of a number divided by twelve is the same as one less than three times its reciprocal.
\n" ); document.write( ":
\n" ); document.write( "Let x = a number
\n" ); document.write( "then
\n" ); document.write( "-x = additive inverse of a number
\n" ); document.write( ":
\n" ); document.write( "Write an equation for the statement:
\n" ); document.write( "\"the additive inverse of a number divided by twelve is the same as one less than three times its reciprocal.\"
\n" ); document.write( " $\"%28-x%29%2F12\"$ = $\"3%2Fx\"$ - 1
\n" ); document.write( "Multiply equation by 12x to get rid of the denominators, and you have:
\n" ); document.write( "x(-x) = 12(3) - 12x
\n" ); document.write( ":
\n" ); document.write( "-x^2 = 36 - 12x
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\n" ); document.write( "Arrange as a quadratic equation:
\n" ); document.write( "x^2 - 12x + 36 = 0
\n" ); document.write( "Factors to
\n" ); document.write( "(x-6)^2 = 0
\n" ); document.write( "x = +6
\n" ); document.write( ":
\n" ); document.write( "Check solution in original equation:
\n" ); document.write( " $\"%28-6%29%2F12\"$ = $\"3%2F6\"$ - 1
\n" ); document.write( " $\"-1%2F2\"$ = $\"1%2F2\"$ - 1; confirms our solution \n" ); document.write( "

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