document.write( "Question 1139391: Solution set and graph for...
\n" ); document.write( "| 2 ( | x - 3 | ) - 7 | < 5 \n" ); document.write( "

Algebra.Com's Answer #759908 by ikleyn(52778) $\"\"$ $\"About$

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document.write( "    | 2*(|x-3|)-7 | < 5\r\n" );
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document.write( "is equivalent to\r\n" );
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document.write( "    -5 < 2*|x-3| - 7 < 5\r\n" );
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document.write( "is equivalent  (after adding 7 to each of 3 parts of the inequality)\r\n" );
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document.write( "    -5 + 7 < 2*|x-3| < 5 + 7\r\n" );
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document.write( "is the same as\r\n" );
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document.write( "    2 < 2*|x-3| < 12    \r\n" );
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document.write( "is equivalent to   (after dividing all the three terms of the inequality by 2)\r\n" );
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document.write( "    1 < |x-3| < 6.\r\n" );
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document.write( "The solutions to the last inequality are those values of x (those numbers or points in the number line) \r\n" );
document.write( "that are remoted from the point x= 3 farther than 1 unit and closer than 6 units.\r\n" );
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document.write( "Obviously, these points (numbers, solutions) are \r\n" );
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document.write( "    -3 < x < 2   and/or  4 < x < 9.\r\n" );
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document.write( "ANSWER.  The solution set to the original inequality is the union  of two intervals  {-3,2)  and  (4,9):  (-3,2) U (4,9).\r\n" );
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