document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=147109>Question 147109</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help solving problems such as<BR>\n" );
document.write( "3y -3 <  5y – 4\r<BR>\n" );
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document.write( "I start with 3y – 3 < 5y<BR>\n" );
document.write( "I am never sure if I should subtract 5y from each side or subtract 3y from each side.\r<BR>\n" );
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document.write( "Then with 3 < 5y – 4<BR>\n" );
document.write( "Do I add four on both sides or subtract 3 from each side?\r<BR>\n" );
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document.write( "I will get different answers depending on which way I go.\r<BR>\n" );
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document.write( "Can you help?\r<BR>\n" );
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document.write( "Thank you.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #107447 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=107447\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y-3%3C5y-4 ALIGN=MIDDLE  ALT=\"3y-3%3C5y-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given inequality.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y%3C5y-4%2B3 ALIGN=MIDDLE  ALT=\"3y%3C5y-4%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y-5y%3C-4%2B3 ALIGN=MIDDLE  ALT=\"3y-5y%3C-4%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5y ALIGN=MIDDLE  ALT=\"5y\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2y%3C-4%2B3 ALIGN=MIDDLE  ALT=\"-2y%3C-4%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the left side.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2y%3C-1 ALIGN=MIDDLE  ALT=\"-2y%3C-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the right side.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3E%28-1%29%2F%28-2%29 ALIGN=MIDDLE  ALT=\"y%3E%28-1%29%2F%28-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2 ALIGN=MIDDLE  ALT=\"-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to isolate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" >. note: Remember, the inequality sign flips when we divide both sides by a negative number. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3E1%2F2 ALIGN=MIDDLE  ALT=\"y%3E1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce.\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So the answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3E1%2F2 ALIGN=MIDDLE  ALT=\"y%3E1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Which approximates to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3E0.5 ALIGN=MIDDLE  ALT=\"y%3E0.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "So the answer in interval notation is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(\frac{1}{2},\infty\right)\">\r<BR>\n" );
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document.write( "Also, the answer in set-builder notation is  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left\{y\|y>\frac{1}{2}\right\}\">\r<BR>\n" );
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document.write( "Here's the graph of the solution set\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28500%2C80%2C-9%2C+11%2C-10%2C+10%2C%0D%0Anumber_line%28+500%2C+-9%2C+11%29%2C%0D%0A%0D%0Aarrow%281%2F2%2C0%2C11%2C0%29%2C%0D%0Aarrow%281%2F2%2C0.30%2C11%2C0.30%29%2C%0D%0Aarrow%281%2F2%2C0.15%2C11%2C0.15%29%2C%0D%0Aarrow%281%2F2%2C-0.15%2C11%2C-0.15%29%2C%0D%0Aarrow%281%2F2%2C-0.30%2C11%2C-0.30%29%2C%0D%0A%0D%0Acircle%281%2F2%2C0%2C0.3%29%2C%0D%0Acircle%281%2F2%2C0%2C0.3%29%2C%0D%0Acircle%281%2F2%2C0%2C0.3%29%2C%0D%0Acircle%281%2F2%2C0%2C0.3-0.02%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Note: there is an <b>open</b> circle at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1%2F2 ALIGN=MIDDLE  ALT=\"y=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > which means that we're excluding that value from the solution set. </SPAN>\n" );
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