document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=222324>Question 222324</A>: <I><SPAN STYLE=\"word-break: break-all;\"> determine the values (write a compound inequality) of x that gives the triangle below a perimeter of no more then 100 and no less than 28. for the \r<BR>\n" );
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document.write( "left side of triangle 4(x-3)<BR>\n" );
document.write( "right side of triangle 3x<BR>\n" );
document.write( "bottom of triangle 5x + 4 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #166480 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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/cgi-bin/show-face.mpl?user=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=166480\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "The perimeter of a triangle is the sum of the measures of the three sides, so for your triangle,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ P\ =\ 4(x -3) + 3x + 5x + 4\">\r<BR>\n" );
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document.write( "Simplify:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ P\ =\ 12x - 8\">\r<BR>\n" );
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document.write( "The perimeter can be no more than 100, so it is less than or equal to 100 and no less than 28, so it is greater than or equal to 28, so:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 28 \leq 12x - 8 \leq 100\">\r<BR>\n" );
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document.write( "Add 8 to all three parts of the compound inequality:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 36 \leq 12x \leq 108\">\r<BR>\n" );
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document.write( "Divide all three parts of the compound inequality by 12:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 3 \leq x \leq 9\">\r<BR>\n" );
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document.write( "However, we have to change the inequality sign on the low end of the interval.  That is because <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x \neq 3\">.  If <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x = 3\"> then the measure of the left side of the triangle would be 0, i.e. <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 4(3 - 3) = 0\">, and there would be no triangle.\r<BR>\n" );
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document.write( "Hence, the final interval for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\"> is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 3 < x \leq 9\">\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
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