document.write( "Question 628344: question: (! = absolute value bars)
\n" ); document.write( "!16-3x!=4x-12\r
\n" ); document.write( "\n" ); document.write( "i keep getting -4 =x and 28=x
\n" ); document.write( "but the answer key states just 4? \n" ); document.write( "
Algebra.Com's Answer #395576 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Equations involving absolute values or square roots often\r\n" );
document.write( "have extraneous answers.  (Answers that don't check in the\r\n" );
document.write( "original equations, and thus are not solutions).  This\r\n" );
document.write( "is such a case.  Let's go through the whole thing:\r\n" );
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document.write( "|16 - 3x| = 4x - 12\r\n" );
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document.write( "Case 1: when 16-3x equals the value of the right side.\r\n" );
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document.write( "16 - 3x = 4x - 12\r\n" );
document.write( "    -7x = -28\r\n" );
document.write( "      x = 4\r\n" );
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document.write( "Case 2: when 16-3x equals -1 times the value of the right side.\r\n" );
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document.write( "16 - 3x = -(4x - 12)\r\n" );
document.write( "    -7x = -4x + 12\r\n" );
document.write( "    -3x = 12\r\n" );
document.write( "      x = -4\r\n" );
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document.write( "You are right except for one thing.  You must check absolute\r\n" );
document.write( "value equations for extraneous solutions. If you check x=4,\r\n" );
document.write( "you will find that it is a solution:\r\n" );
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document.write( "Checking x = 4,\r\n" );
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document.write( "   |16-3x| = 4x-12\r\n" );
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document.write( " |16-3(4)| = 4(4)-12\r\n" );
document.write( " |16 - 12| = 16 - 12\r\n" );
document.write( "       |4| = 4\r\n" );
document.write( "         4 = 4\r\n" );
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document.write( "That checks.  So 4 is a solution.\r\n" );
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document.write( "But watch what happens when we try checking x = -4 in the\r\n" );
document.write( "original equation:\r\n" );
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document.write( "   |16-3x| = 4x-12\r\n" );
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document.write( "|16-3(-4)| = 4(-4)-12\r\n" );
document.write( " |16 + 12| = -16 - 12\r\n" );
document.write( "      |28| = -28\r\n" );
document.write( "        28 = -28\r\n" );
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document.write( "So, as you see that does not check. So -4 must be discarded\r\n" );
document.write( "since it is not a solution.\r\n" );
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document.write( "[Incidentally the absolute value bars are on your keyboard,\r\n" );
document.write( "just above the ENTER key and below the Backspace key. Hold\r\n" );
document.write( "down the shift and press the key for the backward slash \.\r\n" );
document.write( "What's printed on the key looks like two small vertical dashes,\r\n" );
document.write( "one above the other, but it types as |.\r\n" );
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document.write( "Edwin

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