document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=972477>Question 972477</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If x is less than or equal to 7, then the absolute value of the expression x-7 = ?\r<BR>\n" );
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document.write( "The answer is -x+7. I solved it by removing the absolute value bars, which gave me x-7, and -(x-7) = -x+7.\r<BR>\n" );
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document.write( "But, I don't understand what this means. Can anyone explain this to me? What does it mean and why? \r<BR>\n" );
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document.write( "Thank you for any help anyone can give. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #594879 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=594879\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <i>If x is less than or equal to 7, then the absolute value of the expression x-7 = ?<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C=7 ALIGN=MIDDLE  ALT=\"x%3C=7\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "Allows x to be assigned as any of 7 or less than 7.\r<BR>\n" );
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document.write( "Try a step:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-7%3C=7-7 ALIGN=MIDDLE  ALT=\"x-7%3C=7-7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-7%3C=0 ALIGN=MIDDLE  ALT=\"x-7%3C=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "again, for any x less than 7, this expression on the left will be less than zero, and this is expected as first given condition, \"x is less than or equal to 7...\".\r<BR>\n" );
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document.write( "Next part:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28x-7%29=what ALIGN=MIDDLE  ALT=\"abs%28x-7%29=what\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Already established, is that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C=7 ALIGN=MIDDLE  ALT=\"x%3C=7\"   DISABLED_style= \"max-width:90%; height:auto;\" >; which means, x-7 WILL BE NEGATIVE, or in other words, x-7<0, or may be zero.<BR>\n" );
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document.write( "Thinking carefully of the meaning of absolute value,  for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-7%3C=0 ALIGN=MIDDLE  ALT=\"x-7%3C=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28x-7%29=-%28x-7%29 ALIGN=MIDDLE  ALT=\"abs%28x-7%29=-%28x-7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >;<BR>\n" );
document.write( "Again, you need to think through the meaning of absolute value; and drawing this graphed on a number line will help, if needed.\r<BR>\n" );
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document.write( "Try this thought:<BR>\n" );
document.write( "Let p be a positive real number.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28p%29=p ALIGN=MIDDLE  ALT=\"abs%28p%29=p\"   DISABLED_style= \"max-width:90%; height:auto;\" >, nothing too complicated.  p is p units away from zero on the number line, and because p was given as POSITIVE, p is p units TO THE RIGHT OF ZERO.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-p ALIGN=MIDDLE  ALT=\"-p\"   DISABLED_style= \"max-width:90%; height:auto;\" > is also p units AWAY FROM 0 on the number line but <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-p ALIGN=MIDDLE  ALT=\"-p\"   DISABLED_style= \"max-width:90%; height:auto;\" > is to the left of zero.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28-p%29 ALIGN=MIDDLE  ALT=\"abs%28-p%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >-----------What about this?<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28-p%29=-%28-p%29 ALIGN=MIDDLE  ALT=\"abs%28-p%29=-%28-p%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-p ALIGN=MIDDLE  ALT=\"-p\"   DISABLED_style= \"max-width:90%; height:auto;\" > is negative.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28-p%29=-%28-p%29=p ALIGN=MIDDLE  ALT=\"abs%28-p%29=-%28-p%29=p\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "p is a positive number, and -p is a negative number.\r<BR>\n" );
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document.write( "Try examening on your own this one:<BR>\n" );
document.write( "Let r be a negative real number, or let r be real number such that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%3C0 ALIGN=MIDDLE  ALT=\"r%3C0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "--<BR>\n" );
document.write( "What is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28r%29 ALIGN=MIDDLE  ALT=\"abs%28r%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ? </SPAN>\n" );
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