document.write( "Question 988807: Solve for x in the inequality:
\n" ); document.write( "-1 is less than (x+2)/(x-3)\r
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\n" ); document.write( "\n" ); document.write( "Any tips, tricks, advice for other inequality problems is greatly appreciated as well as help with this problem! Thank you in advance! \n" ); document.write( "
Algebra.Com's Answer #609269 by MathTherapy(10552)\"\" \"About 
You can put this solution on YOUR website!

\n" ); document.write( "Solve for x in the inequality:
\n" ); document.write( "-1 is less than (x+2)/(x-3)\r
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\n" ); document.write( "\n" ); document.write( "Any tips, tricks, advice for other inequality problems is greatly appreciated as well as help with this problem! Thank you in advance!
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\"-+1+%3C+%28x+%2B+2%29%2F%28x+-+3%29\", with \"x+%3C%3E+3\" as this would make the denominator 0, and therefore, an UNDEFINED inequality 
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document.write( "\"-+1%28x+-+3%29+%3C+x+%2B+2\" ----- Multiplying both sides by LCD, x - 3
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document.write( "\"-+x+%2B+3+%3C+x+%2B+2\"
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document.write( "\"-+x+%3C+x+%2B+2+-+3\" -------- Subtracting 3 from both sides
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document.write( "\"-+x+%3C+x+-+1\"
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document.write( "\"-+x+-+x+%3C+-+1\" --------- Subtracting x from both sides
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document.write( "\"-+2x+%3C+-+1\"
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document.write( "\"%28-+2x%29%2F%28-+2%29+%3E+%28-+1%29%2F%28-+2%29\" -------- Inequality sign changes when dividing by a negative value
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document.write( "\"x+%3E+1%2F2\"
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document.write( "Now, we have the CRITICAL VALUES: \"system%28%281%2F2%29_and%2C3%29\" 
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document.write( "This means that we will have THREE (3) TEST-INTERVALS to determine whether or not values
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document.write( "in the intervals SATISFY the ORIGINAL inequality: \"-+1+%3C+%28x+%2B+2%29%2F%28x+-+3%29\". These TEST INTERVALS are:
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document.write( "1)   \"x+%3C+1%2F2\"
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document.write( "2)   \"1%2F2+%3C+x+%3C+3\", and
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document.write( "3)   \"x+%3E+3\"\r
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document.write( "Testing \"x+%3C+1%2F2\" with test value: \"x+=+0\", \"-+1+%3C+%28x+%2B+2%29%2F%28x+-+3%29\" becomes: \"-+1+%3C+%280+%2B+2%29%2F%280+-+3%29\"
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document.write( "\"-+1+%3C+2%2F%28-+3%29\"
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document.write( "\"-+1+%3C+-+2%2F3\"
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document.write( "As the above is TRUE, the test-interval: \"highlight_green%28x+%3C+1%2F2%29\" IS a solution\r
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document.write( "Testing \"1%2F2+%3C+x+%3C+3\" with test value: \"x+=+1\", \"-+1+%3C+%28x+%2B+2%29%2F%28x+-+3%29\" becomes: \"-+1+%3C+%281+%2B+2%29%2F%281+-+3%29\"
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document.write( "\"-+1+%3C+3%2F%28-+2%29\"
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document.write( "\"-+1+%3C+-+1%261%2F2\"
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document.write( "As the above is FALSE, the test-interval: \"1%2F2+%3C+x+%3C+3\" IS NOT a solution\r
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document.write( "Testing \"x+%3E+3\" with test value: \"x+=+4\", \"-+1+%3C+%28x+%2B+2%29%2F%28x+-+3%29\" becomes: \"-+1+%3C+%284+%2B+2%29%2F%284+-+3%29\"
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document.write( "\"-+1+%3C+6%2F1\"
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document.write( "\"-+1+%3C+6\"
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document.write( "As the above is TRUE, the test-interval: \"highlight_green%28x+%3E+3%29\" IS a solution
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document.write( "In interval notation, this is: (- oo, ½) ᑌ (3, oo) , or (\"-+infinity\"\"%22%2C%22\"\"1%2F2\") ᑌ (\"3\"\"%22%2C%22\"\"infinity\") \n" );
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