document.write( "Question 898933: 0<(9x-27)^-1<1/9 \n" ); document.write( "
Algebra.Com's Answer #803403 by ikleyn(52794)\"\" \"About 
You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "            The solution by  @CubeyThePenguin is  INCORRECT.\r
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document.write( "You start from this inequality\r\n" );
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document.write( "    0 < (9x-27)^(-1) < 1/9\r\n" );
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document.write( "It is equivalent to the system of two inequalities\r\n" );
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document.write( "    0 < (9x-27)^(-1)          (1)\r\n" );
document.write( "and\r\n" );
document.write( "        (9x-27)^(-1) < 1/9    (2)\r\n" );
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document.write( "connected with the service word \"and\".\r\n" );
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document.write( "First inequality (1)  is  0 < \"1%2F%289x-27%29\";  it is equivalent to  9x - 27 > 0;  x - 3 > 0  and finally  x > 3.\r\n" );
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document.write( "        So for what is follows, we can assume x > 3.     (3)\r\n" );
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document.write( "Second inequality (2)  is  \"1%2F%289x-27%29\" < 1/9;  it is equivalent to  \"1%2F%28x-3%29\" < 1  and finally \r\n" );
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document.write( "(taking into account that x > 3) it implies  1 < x-3; hence x > 4.   (4)\r\n" );
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document.write( "Thus we get the final answer  x > 4.\r\n" );
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document.write( "ANSWER.  The solution set is  x > 4.\r\n" );
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document.write( "                         Visual CHECK\r\n" );
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document.write( "       \r\n" );
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document.write( "      Figure.  Plot y = \"1%2F%289x-27%29\" (red)  and y = \"1%2F9\" (green)\r\n" );
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