document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=95746>Question 95746</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have a problem with my homework. the answer in the book is not matching what I have come up with. I have even had my 9th grader work the problem and she comes up with the same answer. I know that I have done the work right as this is the only problem I have trouble with and all of the other problems have the same answer. I will give you the problem and then show what I did. could you just check my work.<BR>\n" );
document.write( "3/5x-2<3/10-x\r<BR>\n" );
document.write( "\n" );
document.write( "    3/5x-2<3/10-x<BR>\n" );
document.write( "        +x     +x<BR>\n" );
document.write( "        +2     +2<BR>\n" );
document.write( "    3/5x+x<3/10+2<BR>\n" );
document.write( "    3/5x+x<23/10<BR>\n" );
document.write( "    then divided 3/5x by 3/5 <BR>\n" );
document.write( "    and divided 23/10 by 3/5<BR>\n" );
document.write( "    flipped the 3/5 and multiplied the two fractions on the right like this...<BR>\n" );
document.write( "    x+x<23/10*5/3<BR>\n" );
document.write( "    2x<115/30<BR>\n" );
document.write( "    then divided the 2x by 2<BR>\n" );
document.write( "    and the 115/30 by 2 <BR>\n" );
document.write( "    flipped the 2/1 to 1/2 and multiplied 1/2 with 115/30 like this...<BR>\n" );
document.write( "    x<115/30*1/2<BR>\n" );
document.write( "    x<115/60<BR>\n" );
document.write( "    which simplifies to...<BR>\n" );
document.write( "    x<23/12.<BR>\n" );
document.write( "    (-infinity,23/12)\r<BR>\n" );
document.write( "\n" );
document.write( "The problem is the answer in the back of my book is (-infinity,23/16).<BR>\n" );
document.write( "I have checked the problem in the book and the answer many times. Are my calculations correct? <BR>\n" );
document.write( "Thank you...<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #69762 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=69762\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2F5%29x-2%3C3%2F10-x ALIGN=MIDDLE  ALT=\"%283%2F5%29x-2%3C3%2F10-x\"   DISABLED_style= \"max-width:90%; height:auto;\" > <==== OK<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2F5%29x-2%3C3%2F10-x ALIGN=MIDDLE  ALT=\"%283%2F5%29x-2%3C3%2F10-x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "+x +x <==== adding x to both sides OK<BR>\n" );
document.write( "+2 +2 <=== and adding 2 to both sides OK<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2F5%29x%2Bx%3C%283%2F10%29%2B2 ALIGN=MIDDLE  ALT=\"%283%2F5%29x%2Bx%3C%283%2F10%29%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > <==== OK<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2F5%29x%2Bx%3C23%2F10+ ALIGN=MIDDLE  ALT=\"%283%2F5%29x%2Bx%3C23%2F10+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <==== OK<BR>\n" );
document.write( ".<BR>\n" );
document.write( "then divided 3/5x by 3/5 <=== Nope.  You forgot the +x on the left side. When you add <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2F5%29x+%2B+x+=+%283%2F5%29x+%2B+%285%2F5%29x ALIGN=MIDDLE  ALT=\"%283%2F5%29x+%2B+x+=+%283%2F5%29x+%2B+%285%2F5%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" > you get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%288%2F5%29x ALIGN=MIDDLE  ALT=\"%288%2F5%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" > on the left side. At this point<BR>\n" );
document.write( "the equation becomes: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%288%2F5%29x+%3C23%2F10 ALIGN=MIDDLE  ALT=\"%288%2F5%29x+%3C23%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "and divided 23/10 by 3/5 <==== divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2F5 ALIGN=MIDDLE  ALT=\"8%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > to solve for x<BR>\n" );
document.write( ".<BR>\n" );
document.write( "flipped the 3/5 (should flip the 8/5) and multiplied the two fractions on the right like this...<BR>\n" );
document.write( ".<BR>\n" );
document.write( "x+x<23/10*5/3 <=== should be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%2F8%29%2A%288%2F5%29x+%3C+%285%2F8%29%2A+%2823%2F10%29 ALIGN=MIDDLE  ALT=\"%285%2F8%29%2A%288%2F5%29x+%3C+%285%2F8%29%2A+%2823%2F10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "2x<115/30 <=== disregard this. In the preceding step do the multiplication of both sides<BR>\n" );
document.write( "by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F8 ALIGN=MIDDLE  ALT=\"5%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >. The left side becomes just x because in the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%2F8%29%2A%288%2F5%29 ALIGN=MIDDLE  ALT=\"%285%2F8%29%2A%288%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > the<BR>\n" );
document.write( "numerators <BR>\n" );
document.write( "cancel the denominators.  On the other side (the right side) the 5 in the numerator<BR>\n" );
document.write( "reduces the 10 in the denominator to 2 ... so the multiplication becomes just:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2A23%29%2F%288%2A2%29 ALIGN=MIDDLE  ALT=\"%281%2A23%29%2F%288%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and this simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=23%2F16 ALIGN=MIDDLE  ALT=\"23%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So the inequality is reduced to:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%3C+23%2F16 ALIGN=MIDDLE  ALT=\"x+%3C+23%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( ".<BR>\n" );
document.write( "the interpretation of this is that x can take any value less than <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=23%2F16 ALIGN=MIDDLE  ALT=\"23%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" > ... all the<BR>\n" );
document.write( "way down to -infinity. So the answer is (-infinity,23/16)<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Hope this helps you to understand the minor error you made.  When you had <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2F5%29x+%2B+x ALIGN=MIDDLE  ALT=\"%283%2F5%29x+%2B+x\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "you couldn't just divide the one term containing x by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F5 ALIGN=MIDDLE  ALT=\"3%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >. You either had to add the<BR>\n" );
document.write( "two terms containing x or you also had to divide the x by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F5 ALIGN=MIDDLE  ALT=\"3%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );