document.write( "Question 651978: Hello,
\n" ); document.write( "I need to see the steps to solving this equation: |z+8| = |z-3|
\n" ); document.write( "my text book said the answer is -5/2.\r
\n" ); document.write( "\n" ); document.write( "I am just not getting that result. Help please. \n" ); document.write( "

Algebra.Com's Answer #407867 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( " |z+8| = |z-3|\r\n" );
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document.write( "To remove the absolute value bars | |, we break it into two\r\n" );
document.write( "equations, \r\n" );
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document.write( "(1) where the expressions inside that absolute values have THE\r\n" );
document.write( "SAME sign,\r\n" );
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document.write( "and\r\n" );
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document.write( "(2) where the expressions inside that absolute values have OPPOSITE\r\n" );
document.write( "signs.\r\n" );
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document.write( "We examine case (1), which is\r\n" );
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document.write( "   z + 8 = z - 3\r\n" );
document.write( "      \r\n" );
document.write( "Subtract z from both sides and we have\r\n" );
document.write( "      \r\n" );
document.write( "       8 = -3\r\n" );
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document.write( "Which is false and shows that case (1) has no solution. \r\n" );
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document.write( "So we examine case (2), which is found by multiplying one\r\n" );
document.write( "side by (-1), so they will have opposite signs:\r\n" );
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document.write( "   z + 8 = -1(z - 3)\r\n" );
document.write( "   z + 8 = -z + 3\r\n" );
document.write( "      \r\n" );
document.write( "Add z to both sides and we have\r\n" );
document.write( "      \r\n" );
document.write( "  2z + 8 = 3\r\n" );
document.write( "      \r\n" );
document.write( "Subtracting 8 from both sides:\r\n" );
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document.write( "      2z = -5\r\n" );
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document.write( "Dividing both sides by 2:\r\n" );
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document.write( "       z = \r\n" );
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document.write( "So this absolute value equation has only one solution, since \r\n" );
document.write( "case (1) turned out to have no solution.\r\n" );
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document.write( "Edwin

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