document.write( "Question 1138634: \"%28x-2%29%2F%28x%2B5%29%3E=3\" please show your work \n" ); document.write( "
Algebra.Com's Answer #756445 by Edwin McCravy(20063)\"\" \"About 
You can put this solution on YOUR website!
\"%28x-2%29%2F%28x%2B5%29%3E=3\"\r\n" );
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document.write( "We want to multiply through by the LCD of x+5.\r\n" );
document.write( "But if x+5 is negative, the inequality symbol will reverse.\r\n" );
document.write( "So we must take two cases:\r\n" );
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document.write( "Case 1:  x+5>0 or x>-5\r\n" );
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document.write( "\"%28x-2%29%2F%28x%2B5%29%3E=3\"\r\n" );
document.write( "We are multiplying through by a positive number, so we keep\r\n" );
document.write( "the same inequality symbol\r\n" );
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document.write( "\"x-2%3E=3%28x%2B5%29\"\r\n" );
document.write( "\"x-2%3E=3x%2B15\"\r\n" );
document.write( "\"-2x%3E=17\"\r\n" );
document.write( "\"x%3C=-17%2F2\"\r\n" );
document.write( "\"x%3C=-8.5\"\r\n" );
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document.write( "This contradicts x>-5, so Case 1 must be discarded.\r\n" );
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document.write( "Case 2:  x+5<0 or x<-5\r\n" );
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document.write( "\"%28x-2%29%2F%28x%2B5%29%3E=3\"\r\n" );
document.write( "We are multiplying through by a negative number, so we reverse\r\n" );
document.write( "the inequality symbol\r\n" );
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document.write( "\"x-2%3C=3%28x%2B5%29\"\r\n" );
document.write( "\"x-2%3C=3x%2B15\"\r\n" );
document.write( "\"-2x%3C=17\"\r\n" );
document.write( "\"x%3E=-17%2F2\"\r\n" );
document.write( "\"x%3E=-8.5\"\r\n" );
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document.write( "However, case 2 requires that x<-5\r\n" );
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document.write( "So the graph of the solution is\r\n" );
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document.write( "\"matrix%281%2C3%2Cx%3E=-8.5%2CAND%2Cx%3C-5%29\"\r\n" );
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document.write( "which can be written as\r\n" );
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document.write( "\"-8.5%3C=x%3C-5\"\r\n" );
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document.write( "or in interval notation as\r\n" );
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document.write( "[-8,-5)\r\n" );
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document.write( "A bracket on the left to show that -8 is included\r\n" );
document.write( "and a parenthesis on the right.\r\n" );
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document.write( "Edwin
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