document.write( "Question 203853: Find 4 consecutive odd integers whose sum is 117.
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Algebra.Com's Answer #153801 by jsmallt9(3758)\"\" \"About 
You can put this solution on YOUR website!
The key to the consecutive integer (or consecutive even or odd integer) problems is the answer to the question: \"How much more is each of these integers from the one before it?\"

\n" ); document.write( "For consecutive integers the answer is: 1
\n" ); document.write( "Then, to write expressions for consecutive integers, make the variable represent the lowest integer and then, for the rest of the integers, keep adding 1:
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document.write( "Lowest:       x\r\n" );
document.write( "Next higher:  x + 1\r\n" );
document.write( "Next higher:  x + 1 + 1 = x + 2\r\n" );
document.write( "Next higher:  x + 2 + 1 = x + 3\r\n" );
document.write( "Next higher:  x + 3 + 1 = x + 4\r\n" );
document.write( "Next higher:  x + 4 + 1 = x + 5\r\n" );
document.write( "etc.\r\n" );
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\n" ); document.write( "For consecutive even (or odd) integers the answer to the key question is: 2.
\n" ); document.write( "Then, to write expressions for consecutive even (or odd) integers, make the variable represent the lowest integer and then, for the rest of the integers, keep adding 2:
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document.write( "Lowest:       x\r\n" );
document.write( "Next higher:  x + 2\r\n" );
document.write( "Next higher:  x + 2 + 2 = x + 4\r\n" );
document.write( "Next higher:  x + 4 + 2 = x + 6\r\n" );
document.write( "Next higher:  x + 6 + 2 = x + 8\r\n" );
document.write( "Next higher:  x + 8 + 2 = x + 10\r\n" );
document.write( "etc.\r\n" );
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\n" ); document.write( "In your problem you want 4 consecutive odd integers so you will use x, x+2, x+4 and x+6. It says their sum is 117. Sum means addition so:
\n" ); document.write( "\"x+%2B+%28x%2B2%29+%2B+%28x%2B4%29+%2B+%28x%2B6%29+=+117\"
\n" ); document.write( "Now we just solve this equation. Start by simplifying:
\n" ); document.write( "\"4x+%2B+12+=+117\"
\n" ); document.write( "Subtract 12 from both sides:
\n" ); document.write( "\"4x+=+105\"
\n" ); document.write( "Divide by 4:
\n" ); document.write( "\"x+=+105%2F4+=+26.25\"
\n" ); document.write( "Since this is not an integer, much less an odd integer, it means the problem, as stated is impossible. There are no 4 odd consecutive integers which add up to 117.
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