document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1003262>Question 1003262</A>: <I><SPAN STYLE=\"word-break: break-all;\"> | 9-3g | less than or equal to 12 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #803346 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13206)</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=803346\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "You have received two responses showing very similar formal algebraic solutions.<br><BR>\n" );
document.write( "For many problems involving absolute values, it is easier to solve the problem by interpreting the statement<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28x-a%29=b ALIGN=MIDDLE  ALT=\"abs%28x-a%29=b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "as meaning the difference between x and a is equal to b.  Then the problem is easily solved on a number line, using the difference as a distance in either of the two directions.<br><BR>\n" );
document.write( "For solving absolute value inequalities, you can think first of the corresponding equation and then use common sense to find the solution to the inequality.<br><BR>\n" );
document.write( "We first need to get the equation with |x-a| alone on one side.  For your problem...<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%289-3g%29=12 ALIGN=MIDDLE  ALT=\"abs%289-3g%29=12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%283g-9%29=12 ALIGN=MIDDLE  ALT=\"abs%283g-9%29=12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Aabs%28g-3%29=12 ALIGN=MIDDLE  ALT=\"3%2Aabs%28g-3%29=12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28g-3%29=4 ALIGN=MIDDLE  ALT=\"abs%28g-3%29=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Interpret that to say \"the distance between g and 3 is 4\".  Then it is easy to determine that 4 either side of 3 on a number line is either -1 or 7.<br><BR>\n" );
document.write( "So -1 and 7 are the solutions to the absolute value EQUATION; now use common sense to see that the solution the inequality is everything between -1 and 7 -- including the end points, since the inequality is less than or equal to.<br><BR>\n" );
document.write( "This way of looking at and solving absolute value inequalities works especially well if the inequality is \"greater than or equal to\".  Having solved the corresponding equation to find that -1 and 7 are the two points that are exactly u units from 3 on a number line, it is easy to see that the solution for \"distance between x and 3 is GREATER than or equal to 4\" will be all the numbers less than or equal to -1 OR all the numbers greater than of equal to 7.<br><BR>\n" );
document.write( "   </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );