document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=33565>Question 33565</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the solution set.<BR>\n" );
document.write( "|2x-2| is < or = to 2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #20068 by </B><A HREF=/tutors/aboutme.mpl?userid=longjonsilver><B>longjonsilver(2297)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=longjonsilver><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=longjonsilver><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=20068\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> y = |2x-2| means 2 straight lines: 2x-2 and -(2x-2). They form a V-shaped graph, as shown:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28300%2C300%2C+-4%2C+6%2C+-2%2C+10%2C+abs%282x-2%29%29+ ALIGN=MIDDLE  ALT=\"+graph%28300%2C300%2C+-4%2C+6%2C+-2%2C+10%2C+abs%282x-2%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The question is asking \"for what values of x is this graph less than or equal to y=2. Lets look at both these graphs:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28300%2C300%2C+-4%2C+6%2C+-2%2C+10%2C+abs%282x-2%29%2C+2%29+ ALIGN=MIDDLE  ALT=\"+graph%28300%2C300%2C+-4%2C+6%2C+-2%2C+10%2C+abs%282x-2%29%2C+2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Looking at the graph, the V-shape is less than or equal to the y=2 horizontal line between x=0 and x=2. These are the answers. Lets now try to get these 2 answers through algebra:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2x-2+%3C=+2+ ALIGN=MIDDLE  ALT=\"+2x-2+%3C=+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2x+%3C=+4+ ALIGN=MIDDLE  ALT=\"+2x+%3C=+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+%3C=+4%2F2+ ALIGN=MIDDLE  ALT=\"+x+%3C=+4%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+%3C=+2+ ALIGN=MIDDLE  ALT=\"+x+%3C=+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-%282x-2%29+%3C=+2+ ALIGN=MIDDLE  ALT=\"+-%282x-2%29+%3C=+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2x-2+%3E=+-2+ ALIGN=MIDDLE  ALT=\"+2x-2+%3E=+-2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > note the < has changed to a ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2x+%3E=+0+ ALIGN=MIDDLE  ALT=\"+2x+%3E=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+%3E=+0+ ALIGN=MIDDLE  ALT=\"+x+%3E=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+%3E=+0+ ALIGN=MIDDLE  ALT=\"+x+%3E=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+%3C=+2+ ALIGN=MIDDLE  ALT=\"+x+%3C=+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0+%3C=+x+%3C=+2+ ALIGN=MIDDLE  ALT=\"+0+%3C=+x+%3C=+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > which matches the findings from the graph\r<BR>\n" );
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document.write( "jon. </SPAN>\n" );
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