document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1193296>Question 1193296</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 2|3x-4|-3|2x+1|<7 <BR>\n" );
document.write( "No decimals please. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #825313 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=825313\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The behavior of the absolute value function changes at the two points where the absolute value expressions are equal to 0.<br><BR>\n" );
document.write( "3x-4=0 --> x=4/3<BR>\n" );
document.write( "2x+1=0 --> x=-1/2<br><BR>\n" );
document.write( "Those two values of x divide the domain into three intervals: x less than -1/2, x between -1/2 and 4/3, and x greater than 4/3.  Look for solutions in each of those intervals.<br><BR>\n" );
document.write( "(1) x less than -1/2....<br><BR>\n" );
document.write( "On this interval, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%283x-4%29=-3x%2B4 ALIGN=MIDDLE  ALT=\"abs%283x-4%29=-3x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%282x%2B1%29=-2x-1 ALIGN=MIDDLE  ALT=\"abs%282x%2B1%29=-2x-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28-3x%2B4%29-3%28-2x-1%29%3C7 ALIGN=MIDDLE  ALT=\"2%28-3x%2B4%29-3%28-2x-1%29%3C7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6x%2B8%2B6x%2B3%3C7 ALIGN=MIDDLE  ALT=\"-6x%2B8%2B6x%2B3%3C7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11%3C7 ALIGN=MIDDLE  ALT=\"11%3C7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "That inequality is clearly never true; so there are no solutions in this interval.<br><BR>\n" );
document.write( "(2) x between -1/2 and 4/3....<br><BR>\n" );
document.write( "On this interval, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%283x-4%29=-3x%2B4 ALIGN=MIDDLE  ALT=\"abs%283x-4%29=-3x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%282x%2B1%29=2x%2B1 ALIGN=MIDDLE  ALT=\"abs%282x%2B1%29=2x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28-3x%2B4%29-3%282x%2B1%29%3C7 ALIGN=MIDDLE  ALT=\"2%28-3x%2B4%29-3%282x%2B1%29%3C7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6x%2B8-6x-3%3C7 ALIGN=MIDDLE  ALT=\"-6x%2B8-6x-3%3C7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-12x%2B5%3C7 ALIGN=MIDDLE  ALT=\"-12x%2B5%3C7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%3C12x ALIGN=MIDDLE  ALT=\"-2%3C12x\"   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-1%2F6 ALIGN=MIDDLE  ALT=\"x%3E-1%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "x=-1/6 is in this interval, so part of the solution set is x between -1/6 and x=4/3<br><BR>\n" );
document.write( "(3) x greater than 4/3....<br><BR>\n" );
document.write( "On this interval, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%283x-4%29=3x-4 ALIGN=MIDDLE  ALT=\"abs%283x-4%29=3x-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%282x%2B1%29=2x%2B1 ALIGN=MIDDLE  ALT=\"abs%282x%2B1%29=2x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%283x-4%29-3%282x%2B1%29%3C7 ALIGN=MIDDLE  ALT=\"2%283x-4%29-3%282x%2B1%29%3C7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x-8-6x-3%3C7 ALIGN=MIDDLE  ALT=\"6x-8-6x-3%3C7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-11%3C7 ALIGN=MIDDLE  ALT=\"-11%3C7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "That inequality is always true, so the entire interval x greater than 4/3 is part of the solution set.<br><BR>\n" );
document.write( "ANSWER: The solution set is (-1/6,infinity)<br><BR>\n" );
document.write( "A graph confirms that answer:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-3%2C3%2C-15%2C15%2C2%2Aabs%283x-4%29-3%2Aabs%282x%2B1%29%2C7%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-3%2C3%2C-15%2C15%2C2%2Aabs%283x-4%29-3%2Aabs%282x%2B1%29%2C7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The value of the absolute value function (red) is less than 7 (green) everywhere to the right of x=-1/6.<br><BR>\n" );
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