document.write( "Question 852452: |3x+2|-|x-3| = 5 \n" ); document.write( "
Algebra.Com's Answer #519747 by Edwin McCravy(20055) $\"\"$ $\"About$
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document.write( "Incidentally you can type absolute value bars || using the\r\n" );
document.write( "key just above the ENTER or RETURN key.  It is the shifted \. \r\n" );
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document.write( "|3x+2|-|x-3| = 5\r\n" );
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document.write( "There are 4 cases to consider, which are all 4 ways to\r\n" );
document.write( "place signs in front on the expressions between the\r\n" );
document.write( "absolute value bars:\r\n" );
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document.write( "+(3x+2)+(x-3) = 5, +(3x+2)-(x-3) = 5, -(3x+2)+(x-3) = 5, -(3x+2)-(x-3) = 5\r\n" );
document.write( "     3x+2+x-3 = 5,      3x+2-x+3 = 5,     -3x-2+x-3 = 5,     -3x-2-x+3 = 5\r\n" );
document.write( "         4x-1 = 5,          2x+5 = 5,         -2x-5 = 5,         -4x+1 = 5\r\n" );
document.write( "           4x = 6,            3x = 0,           -2x = 10,          -4x = 4\r\n" );
document.write( "            x = 6/4,           x = 0              x = -5             x = -1\r\n" );
document.write( "            x = 3/2\r\n" );
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document.write( "We must check for extraneous solutions by substituting into the\r\n" );
document.write( "original equation:\r\n" );
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document.write( "Checking x = 3/2\r\n" );
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document.write( "       |3x+2|-|x-3| = 5\r\n" );
document.write( " |3(3/2)+2|-|3/2-3| = 5\r\n" );
document.write( "|9/2+4/2|-|3/2-6/2| = 5\r\n" );
document.write( "      |13/2|-|-3/2| = 5\r\n" );
document.write( "       (13/2)-(3/2) = 5\r\n" );
document.write( "               10/2 = 5\r\n" );
document.write( "                  5 = 5\r\n" );
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document.write( "So 3/2 is a solution.\r\n" );
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document.write( "Checking x = 0\r\n" );
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document.write( "       |3x+2|-|x-3| = 5\r\n" );
document.write( " |3(0)+2|-|0-3| = 5\r\n" );
document.write( "     |0+2|-|-3| = 5\r\n" );
document.write( "          |2|-3 = 5\r\n" );
document.write( "            2-3 = 5\r\n" );
document.write( "             -1 = 5\r\n" );
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document.write( "So 0 is NOT a solution.\r\n" );
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document.write( "Checking x = -5\r\n" );
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document.write( "       |3x+2|-|x-3| = 5\r\n" );
document.write( "   |3(-5)+2|-|-5-3| = 5\r\n" );
document.write( "       |-15+2|-|-8| = 5\r\n" );
document.write( "            |-13|-8 = 5\r\n" );
document.write( "               13-8 = 5\r\n" );
document.write( "                  5 = 5\r\n" );
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document.write( "So -5 is a solution.\r\n" );
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document.write( "Checking x = -1\r\n" );
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document.write( "       |3x+2|-|x-3| = 5\r\n" );
document.write( "   |3(-1)+2|-|-1-3| = 5\r\n" );
document.write( "        |-3+2|-|-4| = 5\r\n" );
document.write( "             |-1|-4 = 5\r\n" );
document.write( "                1-4 = 5\r\n" );
document.write( "                 -3 = 5\r\n" );
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document.write( "So -1 is NOT a solution\r\n" );
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document.write( "The only solutions are 3/2 and -5\r\n" );
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document.write( "Edwin
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