document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=173123>Question 173123</A>: <I><SPAN STYLE=\"word-break: break-all;\"> -(3*7          < =    -4 power 2 -8(x-2)+7x    < =     -(12*3) <BR>\n" );
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document.write( " 14/2 )                (2/3x + 17y)power 0 +5        -3 power 2\r<BR>\n" );
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document.write( "solve for x <BR>\n" );
document.write( "this is extra credit but I got 50>= x >= 56  which can't be correct?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #127968 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=127968\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'm assuming that the inequality is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%283%2A7%29%2F%2814%2F2%29%3C=%28-4%5E2-8%28x-2%29%2B7x%29%2F%28%28%282%2F3%29x+%2B+17y%29%5E0%2B5%29%3C=-%2812%2A3%29%2F%28-3%5E2%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "First, note that ANY number (except 0) to the zeroth power is 1. So this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%282%2F3%29x+%2B+17y%29%5E0=1 ALIGN=MIDDLE  ALT=\"%28%282%2F3%29x+%2B+17y%29%5E0=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Also, -3*7=-21 and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14%2F2=7 ALIGN=MIDDLE  ALT=\"14%2F2=7\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So the left side goes from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0A-%283%2A7%29%2F%2814%2F2%29 ALIGN=MIDDLE  ALT=\"%0D%0A-%283%2A7%29%2F%2814%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-21%2F7 ALIGN=MIDDLE  ALT=\"-21%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" > which reduces to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3 ALIGN=MIDDLE  ALT=\"-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Also, -12*3=-36 and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%5E2=-9 ALIGN=MIDDLE  ALT=\"-3%5E2=-9\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So the right side goes from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%2812%2A3%29%2F%28-3%5E2%29 ALIGN=MIDDLE  ALT=\"-%2812%2A3%29%2F%28-3%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-36%2F%28-9%29 ALIGN=MIDDLE  ALT=\"-36%2F%28-9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which reduces to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the inequality\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%283%2A7%29%2F%2814%2F2%29%3C=%28-4%5E2-8%28x-2%29%2B7x%29%2F%28%28%282%2F3%29x+%2B+17y%29%5E0%2B5%29%3C=-%2812%2A3%29%2F%28-3%5E2%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "simplifies to \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%3C=%28-4%5E2-8%28x-2%29%2B7x%29%2F%281%2B5%29%3C=4 ALIGN=MIDDLE  ALT=\"-3%3C=%28-4%5E2-8%28x-2%29%2B7x%29%2F%281%2B5%29%3C=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "-----------------------------------------------------\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%3C=%28-4%5E2-8%28x-2%29%2B7x%29%2F%281%2B5%29%3C=4 ALIGN=MIDDLE  ALT=\"-3%3C=%28-4%5E2-8%28x-2%29%2B7x%29%2F%281%2B5%29%3C=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given compound inequality\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%3C=%28-16-8%28x-2%29%2B7x%29%2F%281%2B5%29%3C=4 ALIGN=MIDDLE  ALT=\"-3%3C=%28-16-8%28x-2%29%2B7x%29%2F%281%2B5%29%3C=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square 4 to get 16\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%3C=%28-16-8x%2B16%2B7x%29%2F%281%2B5%29%3C=4 ALIGN=MIDDLE  ALT=\"-3%3C=%28-16-8x%2B16%2B7x%29%2F%281%2B5%29%3C=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%3C=%28-x%29%2F%286%29%3C=4 ALIGN=MIDDLE  ALT=\"-3%3C=%28-x%29%2F%286%29%3C=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-18%3C=-x%3C=24 ALIGN=MIDDLE  ALT=\"-18%3C=-x%3C=24\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply ALL sides by 6\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18%3E=-x%3E=-24 ALIGN=MIDDLE  ALT=\"18%3E=-x%3E=-24\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide ALL sides by -1 to isolate \"x\" (this will flip the signs)\r<BR>\n" );
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document.write( "==================================================================\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So the solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-24%3C=x%3C=18 ALIGN=MIDDLE  ALT=\"-24%3C=x%3C=18\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the answer in interval notation is   <font size=\"8\">[</font><IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \bf{-24,18}\"><font size=\"8\">]</font>\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\{x\|-24 \le x \le 18\right\}\">\r<BR>\n" );
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document.write( "Here's the graph of the solution set on a number line:\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-29%2C+23%2C-10%2C+10%2C%0D%0Anumber_line%28+500%2C+-29%2C+23+%2C-24%2C18%29%2C%0D%0A%0D%0Ablue%28line%28-24%2C0%2C18%2C0%29%29%2C%0D%0Ablue%28line%28-24%2C0.30%2C18%2C0.30%29%29%2C%0D%0Ablue%28line%28-24%2C0.15%2C18%2C0.15%29%29%2C%0D%0Ablue%28line%28-24%2C-0.15%2C18%2C-0.15%29%29%2C%0D%0Ablue%28line%28-24%2C-0.30%2C18%2C-0.30%29%29%0D%0A%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Graph of the solution set\r<BR>\n" );
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document.write( "Note:\r<BR>\n" );
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document.write( "There is a <b>closed</b> circle at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-24 ALIGN=MIDDLE  ALT=\"x=-24\"   DISABLED_style= \"max-width:90%; height:auto;\" > which means that we're including this value in the solution set\r<BR>\n" );
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document.write( "Also, there is a <b>closed</b> circle at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=18 ALIGN=MIDDLE  ALT=\"x=18\"   DISABLED_style= \"max-width:90%; height:auto;\" > which means that we're including this value in the solution set. </SPAN>\n" );
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