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multiples of 7 is 7N, 7(N+1), 7(N+2), and so on, where N is some unspecified integer.
\n" ); document.write( " Find three consecutive multiples of 7 such that the product of -3 and the sum
\n" ); document.write( " of the first and third is 21 less than 5 times the opposite of the second
\n" ); document.write( ":
\n" ); document.write( "Let the three integers be: 7n, 7(n+1), 7(n+2)
\n" ); document.write( ":
\n" ); document.write( "-3(7n + 7(n+2)) = 5(-7(n+1) - 21
\n" ); document.write( ":
\n" ); document.write( "-3(7n + 7n + 14)) = 5(-7(n+1) - 21
\n" ); document.write( ":
\n" ); document.write( "-3(14n + 14)) = 5(-7(n+1) - 21
\n" ); document.write( ":
\n" ); document.write( "-42m - 42 = 5(-7n - 7) - 21
\n" ); document.write( ":
\n" ); document.write( "-42n - 42 = -35n - 35 - 21
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\n" ); document.write( "-42n - 42 = -35n - 56
\n" ); document.write( "Get rid of all those negatives, multiply by -1
\n" ); document.write( "42n + 42 = 35n + 56
\n" ); document.write( ":
\n" ); document.write( "42n - 35n = 56 - 42
\n" ); document.write( ":
\n" ); document.write( "7n = 14
\n" ); document.write( ":
\n" ); document.write( "n = 2
\n" ); document.write( ":
\n" ); document.write( "The three integers 14, 21, 28
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\n" ); document.write( "See if that checks out in the statement;
\n" ); document.write( "\"the product of -3 and the sum of the first and third is 21 less than 5 times the opposite of the second\"\r
\n" ); document.write( "\n" ); document.write( "-3(14+28) = 5(-21) - 21
\n" ); document.write( "-3(42) = -105 - 21
\n" ); document.write( "-126 = - 126; confirms our solution of n=2 \n" ); document.write( "