document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=42763>Question 42763</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need answer to this asap. I'm just not getting these...\r<BR>\n" );
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document.write( "-4<=2(u+3)-8\r<BR>\n" );
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document.write( "The (u+8) is absolute value </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #27868 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=27868\">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=-4+%3C=+2%2Aabs%28u%2B3%29-+8+ ALIGN=MIDDLE  ALT=\"-4+%3C=+2%2Aabs%28u%2B3%29-+8+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "add 8 to both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4+%3C=+2%2Aabs%28u%2B3%29 ALIGN=MIDDLE  ALT=\"4+%3C=+2%2Aabs%28u%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "divide both sides by 2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2+%3C=+abs%28u%2B3%29 ALIGN=MIDDLE  ALT=\"2+%3C=+abs%28u%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I can see that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u+%3E=+-1 ALIGN=MIDDLE  ALT=\"u+%3E=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u+%3C=+-5 ALIGN=MIDDLE  ALT=\"u+%3C=+-5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This problem can only be understood by plotting it.<BR>\n" );
document.write( "plot <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+%3C=+abs%28u%2B3%29 ALIGN=MIDDLE  ALT=\"y+%3C=+abs%28u%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > by plotting<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+%3C=+u+%2B+3 ALIGN=MIDDLE  ALT=\"y+%3C=+u+%2B+3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+%3C=+-u+-+3 ALIGN=MIDDLE  ALT=\"y+%3C=+-u+-+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C+x%2B3%2C+-x-3%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C+x%2B3%2C+-x-3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The plot goes up and to the right with slope = +1, bounces off the u-axis<BR>\n" );
document.write( "at (-3,0), then goes up and to the left with slope = -1, but <BR>\n" );
document.write( "everything below the horizontal line y = 2 must be excluded because<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2+%3C=+abs%28u%2B3%29 ALIGN=MIDDLE  ALT=\"2+%3C=+abs%28u%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. In summary, u can have ANY value except those<BR>\n" );
document.write( "between u = -1 and u = -5. <BR>\n" );
document.write( "Note that, even though (-3,0) is not a valid point, u = -3 is<BR>\n" );
document.write( "the axis of symmetry for the solution.<BR>\n" );
document.write( "You can test this<BR>\n" );
document.write( "Let u = +10<BR>\n" );
document.write( "then y will be 13<BR>\n" );
document.write( "If -3 is the axis of symmetry, y should have the same value on the<BR>\n" );
document.write( "other side of u = -3<BR>\n" );
document.write( "10 - (-3) = 13<BR>\n" );
document.write( "-u - (-3) = 13<BR>\n" );
document.write( "-u = 16<BR>\n" );
document.write( "u = -16<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+%3C=+abs%28u%2B3%29 ALIGN=MIDDLE  ALT=\"y+%3C=+abs%28u%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2B10+%3C=+abs%2810+%2B+3%29 ALIGN=MIDDLE  ALT=\"%2B10+%3C=+abs%2810+%2B+3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2B10+%3C=+abs%2813%29 ALIGN=MIDDLE  ALT=\"%2B10+%3C=+abs%2813%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2B10+%3C=+abs%28-16+%2B+3%29 ALIGN=MIDDLE  ALT=\"%2B10+%3C=+abs%28-16+%2B+3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2B10+%3C=+abs%28-13%29 ALIGN=MIDDLE  ALT=\"%2B10+%3C=+abs%28-13%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The right side shows that u = -3 is an axis of symmetry<BR>\n" );
document.write( "  </SPAN>\n" );
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