document.write( "Question 155198: I do not know how to even begin to solve the following inequality:\r
\n" ); document.write( "\n" ); document.write( "[(x-3)/(x+2)]>2 \n" ); document.write( "
Algebra.Com's Answer #114260 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
I do not know how to even begin to solve the following inequality:
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document.write( "Get 0 on the right:\r\n" );
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document.write( "\"%28x-3%29%2F%28x%2B2%29-2%3E0\"\r\n" );
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document.write( "Write \"2\" as \"2%2F1\" \r\n" );
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document.write( "\"%28x-3%29%2F%28x%2B2%29-2%2F1%3E0\"\r\n" );
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document.write( "Get the LCD of (x+2) and\r\n" );
document.write( "multiply top and bottom of\r\n" );
document.write( "\"2%2F1\" by that:\r\n" );
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document.write( "\"%28x-3%29%2F%28x%2B2%29-2%28x%2B2%29%2F%281%28x%2B2%29%29%3E0\"\r\n" );
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document.write( "\"%28x-3%29%2F%28x%2B2%29-%282x%2B4%29%2F%28x%2B2%29%3E0\"\r\n" );
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document.write( "Combine the numerators over the LCD:\r\n" );
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document.write( "\"%28%28x-3%29-%282x%2B4%29%29%2F%28x%2B2%29%3E0\"\r\n" );
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document.write( "Remove the parentheses in the top:\r\n" );
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document.write( "\"%28%28x-3-2x-4%29%29%2F%28x%2B2%29%3E0\"\r\n" );
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document.write( "Combine like terms:\r\n" );
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document.write( "\"%28%28-x-7%29%29%2F%28x%2B2%29%3E0\"\r\n" );
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document.write( "Find the critical values by setting both\r\n" );
document.write( "the numerator and the denominator equal to\r\n" );
document.write( "zereo and solving:\r\n" );
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document.write( "\"-x-7=0\" gives critical value \"-7\"\r\n" );
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document.write( "\"x%2B2=0\" gives critical value \"-2\"\r\n" );
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document.write( "Indicate the critical values on a number line:\r\n" );
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document.write( " -------------o-------------------o------------------------\r\n" );
document.write( " -10 -9  -8  -7  -6  -5  -4  -3  -2  -1   0   1   2   3   4\r\n" );
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document.write( "Choose a number left of -7, say -8.\r\n" );
document.write( "Substitute it into the original or the factored form.\r\n" );
document.write( "It's easier to use the factored form:\r\n" );
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document.write( "\"%28%28-x-7%29%29%2F%28x%2B2%29%3E0\"\r\n" );
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document.write( "\"%28-%28-8%29-7%29%2F%28%28-8%29%2B2%29%3E0\"\r\n" );
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document.write( "\"%288-7%29%2F%28-8%2B2%29%3E0\"\r\n" );
document.write( " \r\n" );
document.write( "\"1%2F%28-6%29%3E0\"\r\n" );
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document.write( "\"-1%2F6%3E0\"\r\n" );
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document.write( "That is false so we do not shade the part\r\n" );
document.write( "to the left of \"-7\".  We still have the\r\n" );
document.write( "number line\r\n" );
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document.write( " -------------o-------------------o------------------------\r\n" );
document.write( " -10 -9  -8  -7  -6  -5  -4  -3  -2  -1   0   1   2   3   4\r\n" );
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document.write( "Choose a number between -7 and -2, say -3.\r\n" );
document.write( "Substitute it into the original or the factored form.\r\n" );
document.write( "It's easier to use the factored form:\r\n" );
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document.write( "\"%28%28-x-7%29%29%2F%28x%2B2%29%3E0\"\r\n" );
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document.write( "\"%28-%28-3%29-7%29%2F%28%28-3%29%2B2%29%3E0\"\r\n" );
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document.write( "\"%283-7%29%2F%28-3%2B2%29%3E0\"\r\n" );
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document.write( "\"-4%2F%28-1%29%3E0\"\r\n" );
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document.write( "\"4%3E0\"\r\n" );
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document.write( "That is true so we do shade the part between \"-7\"\r\n" );
document.write( "and \"-2\".\r\n" );
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document.write( " -------------o===================o------------------------\r\n" );
document.write( " -10 -9  -8  -7  -6  -5  -4  -3  -2  -1   0   1   2   3   4\r\n" );
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document.write( "Choose a number right of -2, say 0.\r\n" );
document.write( "Substitute it into the original or the factored form.\r\n" );
document.write( "It's easier to use the factored form:\r\n" );
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document.write( "\"%28%28-x-7%29%29%2F%28x%2B2%29%3E0\"\r\n" );
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document.write( "\"%28-%280%29-7%29%2F%28%280%29%2B2%29%3E0\"\r\n" );
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document.write( "\"%280-7%29%2F%280%2B2%29%3E0\"\r\n" );
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document.write( "\"%28-7%29%2F%282%29%3E0\"\r\n" );
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document.write( "\"-7%2F2%3E0\"\r\n" );
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document.write( "That is false so we do not shade the part\r\n" );
document.write( "to the right of \"-2\".  We end up with the\r\n" );
document.write( "number line\r\n" );
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document.write( " -------------o===================o------------------------\r\n" );
document.write( " -10 -9  -8  -7  -6  -5  -4  -3  -2  -1   0   1   2   3   4\r\n" );
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document.write( "We need only test the endpoints of the interval when the\r\n" );
document.write( "symbol of inequality is < or >.\r\n" );
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document.write( "The answer in interval notation is (-7,-2).\r\n" );
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document.write( "Edwin
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