document.write( "Question 1113593: find three consecutive odd integers such that twice the largest increased by 4 times the smallest is not less than 20 less than nine times the middle. \n" ); document.write( "

Algebra.Com's Answer #728648 by KMST(5328) $\"\"$ $\"About$

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Let the integers be
\n" ); document.write( " $\"n-2\"$ , $\"n\"$ , and $\"n%2B2\"$ .
\n" ); document.write( "We can eliminate any even answers later.
\n" ); document.write( "We calculate that
\n" ); document.write( "\"twice the largest\" = $\"2%28n%2B2%29\"$ ,
\n" ); document.write( "\"4 times the smallest\" = $\"4%28n-2%29\"$ ,
\n" ); document.write( "\"twice the largest increased by 4 times the smallest\" = $\"2%28n%2B2%29%2B4%28n-2%29\"$ ,
\n" ); document.write( "and \"20 less than nine times the middle\" = $\"9n-20\"$ .
\n" ); document.write( "
\n" ); document.write( "The problem, says that $\"2%28n%2B2%29%2B4%28n-2%29\"$ \"is not less than\" $\"9n-20\"$ .
\n" ); document.write( "Because it has to be either one way or the other,
\n" ); document.write( "the phrase \"not less than\" means \"more than or equal to\",
\n" ); document.write( "so the inequality to solve is
\n" ); document.write( " $\"2%28n%2B2%29%2B4%28n-2%29%3E=9n-20\"$ .
\n" ); document.write( "
\n" ); document.write( "Solving:
\n" ); document.write( " $\"2%28n%2B2%29%2B4%28n-2%29%3E=9n-20\"$
\n" ); document.write( " $\"2n%2B4%2B4n-8%3E=9n-20\"$
\n" ); document.write( " $\"6n-4%3E=9n-20\"$
\n" ); document.write( " $\"6n-4-6n%2B20%3E=9n-20-6n%2B20\"$
\n" ); document.write( " $\"20-4%3E=9n-6n\"$
\n" ); document.write( " $\"16%3E=3n\"$
\n" ); document.write( " $\"16%2F3%3E=n\"$
\n" ); document.write( " $\"n%3C=16%2F3=5%261%2F3\"$ , along with the fact that
\n" ); document.write( " $\"n\"$ and $\"n-2\"$ are supposed to be (positive) odd integers,
\n" ); document.write( "means that $\"n=5\"$ or $\"n=3\"$ .
\n" ); document.write( "So, the \"three consecutive odd integers\" in the problem are
\n" ); document.write( " $\"highlight%28matrix%281%2C5%2C3%2C%22%2C%22%2C5%2C%22%2C%22%2C7%29%29\"$ or $\"highlight%28matrix%281%2C5%2C1%2C%22%2C%22%2C3%2C%22%2C%22%2C5%29%29\"$ \n" ); document.write( "

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