document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=651624>Question 651624</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am working on an absolute value inequality for my algebra class. The problem is 9[1-z] is less than or equal to -36. For this questions [] represent absolute value. \r<BR>\n" );
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document.write( "To solve this I used two cases of absolute value. <BR>\n" );
document.write( "The first case is -(1-z)=<-4. I added one to each side of the equation to come up with z=<-3. \r<BR>\n" );
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document.write( "The second case is (1-z)=<-4. I added 1 to each side to get -z=<-5. Then I divided by -1. After dividing and flipping the sign I came up with z=>5. \r<BR>\n" );
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document.write( "The answer needs to be in set notation so the answer I came up with was [-3,5]. \r<BR>\n" );
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document.write( "When I submitted my answer it was marked incorrect and I am not sure why. I honestly thought I was doing this correctly and I do not know where I messed up. \r<BR>\n" );
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document.write( "*For this question =< and => represent less than or equal to and greater than or equal to.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #407747 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=407747\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the original equation is:<BR>\n" );
document.write( "9*|1-x| <= -36<BR>\n" );
document.write( "divide both sides of this equation by 9 to get:<BR>\n" );
document.write( "|1-x| <= -36/9 which simplifies to:<BR>\n" );
document.write( "|1-x| <= -4<BR>\n" );
document.write( "this leads to 2 equations:<BR>\n" );
document.write( "(1-x) <= -4<BR>\n" );
document.write( "-(1-x) <= -4<BR>\n" );
document.write( "so far so good.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "solving for (1-x) <= -4:<BR>\n" );
document.write( "remove parentheses to get:<BR>\n" );
document.write( "1-x <= -4<BR>\n" );
document.write( "subtract 1 from both sides of the equation to get:<BR>\n" );
document.write( "-x <= -5<BR>\n" );
document.write( "multiply both sides of the equation by -1 to get:<BR>\n" );
document.write( "x >= 5<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "solving for -(1-x) <= -4:<BR>\n" );
document.write( "remove parentheses to get:<BR>\n" );
document.write( "-1+x <= -4<BR>\n" );
document.write( "add 1 to both sides of the equation to get:<BR>\n" );
document.write( "x <= -3<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "your 2 solutions are:<BR>\n" );
document.write( "x >= 5 or x <= -3<BR>\n" );
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document.write( "this appears to agree with what you derived.<BR>\n" );
document.write( "placing it in interval notation would indicate the following:<BR>\n" );
document.write( "(-infinity,-3] union [5,+infinity)<BR>\n" );
document.write( "i believe this is where you went wrong.<BR>\n" );
document.write( "x <= -3 means that x goes from minus infinity up to and including -3.<BR>\n" );
document.write( "that's where the interval notation of (-infinity,-3] comes in.<BR>\n" );
document.write( "note that this is interval notation and not set notation.<BR>\n" );
document.write( "x >= 5 means that x goes from 5 to plus infinity.  since 5 is included in the solution set, the interval becomes:<BR>\n" );
document.write( "[5,+infinity)<BR>\n" );
document.write( "the (-infinity means that the value is greater than minus infinity.<BR>\n" );
document.write( "the +infinity) means that the value is less than plus infinity.<BR>\n" );
document.write( "the -3] means that the value is less than or equal to -3.<BR>\n" );
document.write( "the [5 means that the value is greater than or equal to 5.<BR>\n" );
document.write( "not again that this is interval notation, not set noation.<BR>\n" );
document.write( "in set notation, the answer would be shown as:<BR>\n" );
document.write( "{x | x <= -3 or x >= 5}<BR>\n" );
document.write( "or:<BR>\n" );
document.write( "{x element of real numbers | x <= -3 or x >= 5}<BR>\n" );
document.write( "i'd say you got the answer correct but displayed it wrong.<BR>\n" );
document.write( "here's a reference on interval notation and set notation.<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"http://www.regentsprep.org/Regents/math/ALGEBRA/AP1/IntervalNot.htm\" target = \"_blank\">http://www.regentsprep.org/Regents/math/ALGEBRA/AP1/IntervalNot.htm</a>\r<BR>\n" );
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document.write( " </SPAN>\n" );
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