document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=66376>Question 66376</A>: <I><SPAN STYLE=\"word-break: break-all;\"> absolute value of x-1 -0.5 is less than or equal to (1/2)x+5\r<BR>\n" );
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document.write( "graph with points  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #47078 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=47078\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> absolute value of x-1 -0.5 is less than or equal to (1/2)x+5<BR>\n" );
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document.write( "|x-1|-0.5 <=(1/2)x+5<BR>\n" );
document.write( "|x-1|<=(1/2)x+5.5<BR>\n" );
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document.write( "Comment: The absolute can have two meanings:<BR>\n" );
document.write( "If x>=1 |x-1|=x-1<BR>\n" );
document.write( "If x<1 |x-1|=-(x-1)<BR>\n" );
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document.write( "So,<BR>\n" );
document.write( "If x>=1, you get x-1<=(1/2)x+5.5<BR>\n" );
document.write( "(1/2)x<=6.5<BR>\n" );
document.write( "x<=13<BR>\n" );
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document.write( "If x<1, you get -(x-1)<=(1/2)x+5.5<BR>\n" );
document.write( "-x+1<=(1/2)x+5.5<BR>\n" );
document.write( "(3/2)x>=-4.5<BR>\n" );
document.write( "x>=-3<BR>\n" );
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document.write( "Final solution:<BR>\n" );
document.write( "-3<=x<=13<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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