document.write( "Question 651699: |x+13|=|x-10| what is the set solution? \n" ); document.write( "
Algebra.Com's Answer #407772 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( " |x+13|=|x-10|\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( "  x + 13 = x - 10\r\n" );
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document.write( "Subtract x from both sides and we have\r\n" );
document.write( "      \r\n" );
document.write( "      13 = -10\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\r\n" );
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document.write( "  x + 13 = -(x - 10)\r\n" );
document.write( "  x + 13 = -x + 10\r\n" );
document.write( "      \r\n" );
document.write( "Add x to both sides and we have\r\n" );
document.write( "      \r\n" );
document.write( " 2x + 13 = 10\r\n" );
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document.write( "Subtracting 13 from both sides:\r\n" );
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document.write( "      2x = -3\r\n" );
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document.write( "Dividing both sides by 2:\r\n" );
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document.write( "       x = \"-3%2F2\"\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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