document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=31488>Question 31488</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0321227573/algebrahomeworkh>College Algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> I have been working on this Rational inequality since Saturday morning and am still miffed.<BR>\n" );
document.write( "Problem: (x/x-2)>=5\r<BR>\n" );
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document.write( "I put the expression into standard from by (x)/(x-2)-5>=0\r<BR>\n" );
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document.write( "I used the LCD to factor and put into one single fraction for(x)-5(x-2)/(x-2)>=0.\r<BR>\n" );
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document.write( "Which gave me: (X-5x-10)/(x-2)>=0\r<BR>\n" );
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document.write( "After combining terms I had: (4x-10)/(x-2)>=0\r<BR>\n" );
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document.write( "Which I then set both numerator and demonitor to be solved for >=0 and arrivd at:\r<BR>\n" );
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document.write( "x>=10/4 or 5/2\r<BR>\n" );
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document.write( "and x-2=0 which is (+2-2)>=0 which is  Undefined and not a solution since a zero in the denominnator can't be a solution.\r<BR>\n" );
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document.write( "So (2,5/2) became the boundary points to test for true and fasle statements.\r<BR>\n" );
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document.write( "This is where I get confused.\r<BR>\n" );
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document.write( "When I plugged this expression into my y= screen on my TI-83 Plus calculator it gave me a vertical asympotote where the solutions I came up with is located on the x-axis.\r<BR>\n" );
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document.write( "When I algebraically used test values for the three intervals of (-00,2) (2,5/2) (5/2,00) I was even more confused because, when I tested using (-2) for the first interval of (00,2) the result was (-4) a value that was not >=5 and for the next test interval of (2,5/2) and used (2.25) as a test value I still get a value less than 5.\r<BR>\n" );
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document.write( "And for the last test inteval of (5/2,00) I used (3) I still get a denominator (3-2) that is less than 5. So none of the solutions I came up with are true statements.\r<BR>\n" );
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document.write( "None of these test values would satisfy the inequality statement of being >= to 5.\r<BR>\n" );
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document.write( "So the only thing I could figure out was that the vertical asymptote must mean some sort of sign change that takes place, but whee in the solution process this takes place is a mystery to me, as I hunted til the cows did not come home trying to find this answer.\r<BR>\n" );
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document.write( "At this rate I will never get this take home quiz finished by Tuesday March 28th.<BR>\n" );
document.write( "Your help in helping me with this task is greatly appreciated. \r<BR>\n" );
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document.write( "My God I have spent some 20 hours since Sat morning and its now nearly midnight Sunday.\r<BR>\n" );
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document.write( "Sincerely,\r<BR>\n" );
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document.write( "Robert S. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #18150 by </B><A HREF=/tutors/aboutme.mpl?userid=venugopalramana><B>venugopalramana(3286)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=venugopalramana><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.geocities.com/venugopalramana/FREE_MATHS_ASSISTANCE.html valign=middle><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=18150\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> SORRY TO NOTE YOUR PLIGHT.THOUGH YOU HAVE PROCEEDED IN A PROPER WAY,I SHALL GIVE YOU AN ALTERNATE ROUTE.SEE IF THAT SUITS YOU.<BR>\n" );
document.write( "Problem: (x/x-2)>=5 ..YOU TRANSFERRED 5 TO LHS WHICH IS THE PROPER WAY IN INEQUALITIES`AS YOU DONOT KNOW ABOUT NATURE OF X AND ITS FUNCTIONS.BUT THERE IS ANOTHER WAY TO GO I AM JUST SHOWING IT TO YOU AS AN ILLUSTRTION<BR>\n" );
document.write( "WE DONT KNOW NATURE OF X-2...SO....<BR>\n" );
document.write( "CASE 1...X-2=0...NOT ALLWED AS THE FUNCTION IS NOT DEFINED THEN.\r<BR>\n" );
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document.write( "CASE.2. .....LET X-2 BE POSITIVE OR X>2..THEN<BR>\n" );
document.write( "X>5(X-2)<BR>\n" );
document.write( "X-5X>-10<BR>\n" );
document.write( "-4X>-10<BR>\n" );
document.write( "4X<10.....AS MULTIPLICATION WITH NEGATIVE NUMBER WILL REVERSE THE INEQUALITY.<BR>\n" );
document.write( "X<10/4=2.5...NOW CHECK WITH OUR ORIGINAL ASSUMPTION THAT X>2..IT IS COMPATABLE...<BR>\n" );
document.write( "HENCE FOR THIS CASE THE SOLUTION IS X>2 BUT <2.5...THAT IS X IS BETWEN 2 AND 2.5<BR>\n" );
document.write( "CASE.3.....LET X-2 BE NEGATIVE...OR....X<2<BR>\n" );
document.write( "X<5(X-2)...AS MULTIPLICATION WITH NEGATIVE NUMBER WILL REVERSE THE INEQUALITY.<BR>\n" );
document.write( "X-5X<-10<BR>\n" );
document.write( "-4X<-10<BR>\n" );
document.write( "4X>10......AS MULTIPLICATION WITH NEGATIVE NUMBER WILL REVERSE THE INEQUALITY.<BR>\n" );
document.write( "X>10/4=2.5..NOW CHECK WITH OUR ORIGINAL ASSUMPTION THAT X<2..IT IS NOT COMPATABLE...<BR>\n" );
document.write( "HENCE FOR THIS CASE THERE IS NO SOLUTION<BR>\n" );
document.write( "HENCE THE TOTAL SOLUTION SET IS <BR>\n" );
document.write( "X LIES BETWEEN 2 AND 2.5<BR>\n" );
document.write( "OK GOT IT .IF STILL IN DOUBT OR YOU WANT TO LEARN MORE PLEASE COME BACK. </SPAN>\n" );
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