document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=112393>Question 112393</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Have I understood this correctly? I get confused very easy at times! I believe this is true. |-8| + |3| = |-8 + 3| Thanks so much for your time. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #82010 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=82010\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's try to straighten out the confusion by using a rule. Whatever the sign of a quantity <BR>\n" );
document.write( "inside the absolute value signs, when you remove the absolute value signs that quantity<BR>\n" );
document.write( "will be positive.<BR>\n" );
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document.write( "So lets start with:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28-8%29+%2B+abs%28%2B3%29 ALIGN=MIDDLE  ALT=\"abs%28-8%29+%2B+abs%28%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "You can remove the absolute value signs around the -8, but when you do that you change it<BR>\n" );
document.write( "to a +8. And you can remove the absolute value signs around the +3, and it remains a +3.<BR>\n" );
document.write( "So the problem becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28-8%29+%2B+abs%28%2B3%29+=+%2B8+%2B+3+=+%2B11 ALIGN=MIDDLE  ALT=\"abs%28-8%29+%2B+abs%28%2B3%29+=+%2B8+%2B+3+=+%2B11\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now let's look at what you believed to be equivalent:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28-8+%2B+3%29 ALIGN=MIDDLE  ALT=\"abs%28-8+%2B+3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "First you have to algebraically combine the terms inside the absolute value signs:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8+%2B+3+=+-5 ALIGN=MIDDLE  ALT=\"-8+%2B+3+=+-5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This converts your answer to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28-5%29 ALIGN=MIDDLE  ALT=\"abs%28-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "And applying the rule ... remove the absolute value signs, and make sure the quantity<BR>\n" );
document.write( "they contained now has a plus sign. This means:<BR>\n" );
document.write( ".\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28-8+%2B+3%29=abs%28-5%29+=+%2B5 ALIGN=MIDDLE  ALT=\"abs%28-8+%2B+3%29=abs%28-5%29+=+%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Notice that the two answers ... +11 and +5 ... are not the same. The correct answer to<BR>\n" );
document.write( "this problem is +11. <BR>\n" );
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document.write( "Hope this helps you to understand absolute values a little better. </SPAN>\n" );
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