document.write( "Question 949423: A couple of questions from my textbook that I need help with. I'm having trouble with rational inequalities. \r
\n" ); document.write( "\n" ); document.write( "Solve the following inequalities and give your answer in interval notation.\r
\n" ); document.write( "\n" ); document.write( "a. -3≤ 3-5x/3 <3/8
\n" ); document.write( "b. 3x-5/x >0\r
\n" ); document.write( "\n" ); document.write( "Hint: Either both the numerator and the denominator are positive, or both are negative; consider both cases.\r
\n" ); document.write( "\n" ); document.write( "Thanks.\r
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Algebra.Com's Answer #580865 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "a. -3≤ 3-5x/3 <3/8\r\n" );
document.write( "b. 3x-5/x >0\r\n" );
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document.write( "When typing algebra, you must put parentheses around \r\n" );
document.write( "numerators and denominators if they contain more than \r\n" );
document.write( "1 letter or 1 number, like this\r\n" );
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document.write( "a. -3≤ (3-5x)/3 <3/8\r\n" );
document.write( "b. (3x-5)/x >0\r\n" );
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document.write( "----------------------------\r\n" );
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document.write( "\"-3%3C=+%283-5x%29%2F3+%3C3%2F8\" \r\n" );
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document.write( "Multiply thru all 3 sides by 24\r\n" );
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document.write( "\"-72%3C=+8%283-5x%29+%3C9\"\r\n" );
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document.write( "\"-72%3C=24-40x+%3C9\"\r\n" );
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document.write( "Add -24 to all 3 sides:\r\n" );
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document.write( "\"-72%3C-40x+%3C9\"\r\n" );
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document.write( "\"-96%3C=-40x%3C-15\"\r\n" );
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document.write( "Divide through by -40 which reverses\r\n" );
document.write( "the inequalities\r\n" );
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document.write( "\"%28-96%29%2F%28-40%29%3E=x%3E%28-15%29%2F%28-40%29\"\r\n" );
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document.write( "\"12%2F5%3E=x%3E-3%2F8\"\r\n" );
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document.write( "-------------------------------\r\n" );
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document.write( "b. (3x-5)/x >0\r\n" );
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document.write( "Critical values are when numerator equas zero and when\r\n" );
document.write( "denominator equals zero.\r\n" );
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document.write( "Numerator=0\r\n" );
document.write( "3x-5 = 0\r\n" );
document.write( "  3x = 5\r\n" );
document.write( "   x = \"5%2F3\" = \"1%262%2F3\"   <-- critical value\r\n" );
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document.write( "Denominator = 0\r\n" );
document.write( "   x = 0\r\n" );
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document.write( "Put critical values on number line:\r\n" );
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document.write( "------------o------o---------------\r\n" );
document.write( "            0     \"5%2F3\"\r\n" );
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document.write( "Test any value less than 0, say -1, by substituting\r\n" );
document.write( "in the original:\r\n" );
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document.write( "\"%283x-5%29%2Fx+%3E+0\"\r\n" );
document.write( "\r\n" );
document.write( "\"%283%5E%22%22%28-1%29-5%29%2F%28-1%29+%3E+0\"\r\n" );
document.write( "\r\n" );
document.write( "\"%28-3-5%29%2F%28-1%29+%3E+0\"\r\n" );
document.write( "\r\n" );
document.write( "\"%28-8%29%2F%28-1%29%3E0\"\r\n" );
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document.write( "\"8%3E0\"\r\n" );
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document.write( "That's true so we shade line left of 0\r\n" );
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document.write( "<===========o------o---------------\r\n" );
document.write( "            0      \"5%2F3\"\r\n" );
document.write( "\r\n" );
document.write( "---------------\r\n" );
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document.write( "Next test any value between 0 and \"5%2F3\", say 1, by substituting\r\n" );
document.write( "in the original:\r\n" );
document.write( "\r\n" );
document.write( "\"%283x-5%29%2Fx+%3E+0\"\r\n" );
document.write( "\r\n" );
document.write( "\"%283%5E%22%22%281%29-5%29%2F%281%29+%3E+0\"\r\n" );
document.write( "\r\n" );
document.write( "\"%283-5%29+%3E+0\"\r\n" );
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document.write( "\"-2%3E0\"\r\n" );
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document.write( "That's false so we do not shade line between 0 and \"5%2F3\". We\r\n" );
document.write( "still have\r\n" );
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document.write( "<===========o------o---------------\r\n" );
document.write( "            0      \"5%2F3\"\r\n" );
document.write( "\r\n" );
document.write( "-----------------\r\n" );
document.write( "\r\n" );
document.write( "Test any value right of \"5%2F3\", say 2, by substituting\r\n" );
document.write( "in the original:\r\n" );
document.write( "\r\n" );
document.write( "\"%283x-5%29%2Fx+%3E+0\"\r\n" );
document.write( "\r\n" );
document.write( "\"%283%5E%22%22%282%29-5%29%2F%282%29+%3E+0\"\r\n" );
document.write( "\r\n" );
document.write( "\"%286-5%29%2F2+%3E+0\"\r\n" );
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document.write( "\"%281%29%2F2%3E0\"\r\n" );
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document.write( "\"1%2F2%3E0\"\r\n" );
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document.write( "That's true so we shade line right of \"5%2F3\"\r\n" );
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document.write( "S\r\n" );
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document.write( "<===========o------o==========>\r\n" );
document.write( "            0      \"5%2F3\"\r\n" );
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document.write( "Interval notation \r\n" );
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document.write( "Edwin
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