document.write( "Question 119683: Three consecutive even integers are such that the product of the first two is 6 less than 9 times the third. Find the integers. \n" ); document.write( "

Algebra.Com's Answer #87678 by tutor_paul(519) $\"\"$ $\"About$

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Put the given words into an equation. Let x be the first even integer. Then x+2 is the next even integer (since you need to add 2 to a given even number to get the next even number), and x+4 is the next even integer:
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\n" ); document.write( " $\"x%28x%2B2%29=9%28x%2B4%29-6\"$
\n" ); document.write( "Multiply through:
\n" ); document.write( " $\"x%5E2%2B2x=9x%2B36-6\"$
\n" ); document.write( "Put the quadratic into standard form:
\n" ); document.write( " $\"x%5E2-7x-30=0\"$
\n" ); document.write( "Factor:
\n" ); document.write( " $\"%28x%2B3%29%28x-10%29=0\"$
\n" ); document.write( "Solve for x:
\n" ); document.write( " $\"x%2B3=0\"$
\n" ); document.write( " $\"x=-3\"$
\n" ); document.write( "Note that this value for x is no good for this problem, since it is an odd number.
\n" ); document.write( " $\"x-10=0\"$
\n" ); document.write( " $\"highlight%28x=10%29\"$
\n" ); document.write( "Remember, x is the first even integer. So the three even integers are:
\n" ); document.write( " $\"10\"$ , $\"12\"$ , $\"14\"$
\n" ); document.write( "You can verify this result to see if the given holds true with these numbers.
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\n" ); document.write( "Good Luck,
\n" ); document.write( "tutor_paul@yahoo.com
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