document.write( "Question 932628: The three terms 7x+1, 9x+7, and 3x-4 (not necessarily in order) are 3 consecutive terms of an arithmetic sequence. Find the largest possible value of the common difference of such an arithmetic sequence. \n" ); document.write( "

Algebra.Com's Answer #567143 by Edwin McCravy(20056) $\"\"$ $\"About$

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document.write( "Try it all 6 possible ways to order them:\r\n" );
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document.write( "(1) 7x+1, 9x+7, 3x-4 \r\n" );
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document.write( "Common difference = (9x+7)-(7x+1) = (3x-4)-(9x+7)\r\n" );
document.write( "                        9x+7-7x-1 = 3x-4-9x-7\r\n" );
document.write( "                             2x+6 = -6x-11\r\n" );
document.write( "                               8x = -17\r\n" );
document.write( "                                x = -17/8 = -2.125\r\n" );
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document.write( "Common difference = 2x+6 = 2(-2.125)+6 = 1.75\r\n" );
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document.write( "(2) 7x+1, 3x-4, 9x+7\r\n" );
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document.write( "Common difference = (3x-4)-(7x+1) = (9x+7)-(3x-4)\r\n" );
document.write( "                        3x-4-7x-1 = 9x+7-3x+4\r\n" );
document.write( "                            -4x-5 = 6x+11\r\n" );
document.write( "                             -10x = 16\r\n" );
document.write( "                                x = 16/(-10) = -8/5 = -1.6\r\n" );
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document.write( "Common difference = -4x-5 = -4(-1.6)-5 = 1.4\r\n" );
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document.write( "(3) 9x+7, 7x+1, 3x-4\r\n" );
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document.write( "Common difference = (7x+1)-(9x+7) = (3x-4)-(7x+1)\r\n" );
document.write( "                        7x+1-9x-7 = 3x-4-7x-1\r\n" );
document.write( "                            -2x-6 = -4x-5\r\n" );
document.write( "                               2x = 1\r\n" );
document.write( "                                x = 1/2 = 0.5\r\n" );
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document.write( "Common difference = -2x-6 = -2(0.5)-6 = -7\r\n" );
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document.write( "(4) 9x+7, 3x-4, 7x+1\r\n" );
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document.write( "Common difference = (3x-4)-(9x+7) = (7x+1)-(3x-4)\r\n" );
document.write( "                        3x-4-9x-7 = 7x+1-3x+4\r\n" );
document.write( "                           -6x-11 = 4x+5\r\n" );
document.write( "                             -10x = 16\r\n" );
document.write( "                                x = 16/(-10) = -8/5 = -1.6\r\n" );
document.write( "                                x = -8/5 = -1.6\r\n" );
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document.write( "Common difference = -6x-11 = -6(-1.6)-11 = -1.4\r\n" );
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document.write( "(5) 3x-4, 7x+1, 9x+7\r\n" );
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document.write( "Common difference = (7x+1)-(3x-4) = (9x+7)-(7x+1)\r\n" );
document.write( "                        7x+1-3x+4 = 9x+7-7x-1\r\n" );
document.write( "                             4x+5 = 2x+6\r\n" );
document.write( "                               2x = 1\r\n" );
document.write( "                                x = 1/2 = 0.5\r\n" );
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document.write( "Common difference = 4x+5 = 4(0.5)+5 = 7\r\n" );
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document.write( "(6) 3x-4, 9x+7, 7x+1\r\n" );
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document.write( "Common difference = (9x+7)-(3x-4) = (7x+1)-(9x+7)\r\n" );
document.write( "                        9x+7-3x+4 = 7x+1-9x-7\r\n" );
document.write( "                            6x+11 = -2x-6\r\n" );
document.write( "                               8x = -17\r\n" );
document.write( "                                x = -17/8 = -2.125\r\n" );
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document.write( "Common difference = 6x+11 = 6(-2.125)+11 = -1.75\r\n" );
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document.write( "Case 5 gives the largesr common difference of 7\r\n" );
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document.write( "Edwin

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