document.write( "Question 1207662: If k = (x + 3)/(x - 4) and k^2 - 3k = 28, find x. \r
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\n" ); document.write( "\n" ); document.write( "I say replace every k with (x + 3)/(x - 4).\r
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\n" ); document.write( "\n" ); document.write( "[(x + 3)/(x - 4)]^2 - 3[(x + 3)/(x - 4)] = 28\r
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Algebra.Com's Answer #845654 by ikleyn(52788) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "If k = (x + 3)/(x - 4) and k^2 - 3k = 28, find x.
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document.write( "First solve the quadratic equation for k and find its solutions for k.\r\n" );
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document.write( "    k^2 - 3k = 28\r\n" );
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document.write( "is equivalent to\r\n" );
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document.write( "    k^2 - 3k - 28 = 0.\r\n" );
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document.write( "Factor left side\r\n" );
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document.write( "    (k-7)*(k+4) = 0.\r\n" );
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document.write( "The solutions are k= 7 and k= -4.\r\n" );
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document.write( "        Now consider and solve equation   = k   \r\n" );
document.write( "        for two values of k: k= 7 and  k= -4.\r\n" );
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document.write( "(a)  Case k = 7.\r\n" );
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document.write( "     Now solve equation\r\n" );
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document.write( "           = 7\r\n" );
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document.write( "     Step by step\r\n" );
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document.write( "          x+3 = 7*(x-4)\r\n" );
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document.write( "          x+3 = 7x - 28\r\n" );
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document.write( "           3 + 28 = 7x - x\r\n" );
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document.write( "            31 = 6x\r\n" );
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document.write( "             x = .\r\n" );
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document.write( "(b)  Case k = -4.\r\n" );
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document.write( "     Now solve equation\r\n" );
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document.write( "           = -4\r\n" );
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document.write( "     Step by step\r\n" );
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document.write( "          x+3 = (-4)*(x-4)\r\n" );
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document.write( "          x+3 = -4x + 16\r\n" );
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document.write( "           x + 4x = 16 - 3\r\n" );
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document.write( "            5x = 13\r\n" );
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document.write( "             x = .\r\n" );
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document.write( "ANSWER.  Two solutions are  x =   and  x = .\r\n" );
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