document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1199369>Question 1199369</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the inequality. \r<BR>\n" );
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document.write( "|-4x| + |-5| ≤ 1\r<BR>\n" );
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document.write( "|-4x| + -5 ≤ 1\r<BR>\n" );
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document.write( "|-4x| + ≤ 1 + 5\r<BR>\n" );
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document.write( "|-4x| ≤ 6\r<BR>\n" );
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document.write( "-6 < -4x < 6\r<BR>\n" );
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document.write( "-6/-4 > x > 6/-4\r<BR>\n" );
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document.write( "3/2 > x > -3/2\r<BR>\n" );
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document.write( "Let S = solution set\r<BR>\n" );
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document.write( "My answer: S = {x | 3/2 > x > -3/2}\r<BR>\n" );
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document.write( "Textbook answer: No solution.\r<BR>\n" );
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document.write( "What did I do wrong? Why is the empty set or no solution the right answer? \r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #833227 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52776)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=833227\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;You are wrong starting from the &nbsp;FIRST &nbsp;LINE &nbsp;of your solution.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The correct solution is as follows.\r<BR>\n" );
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document.write( "Our starting inequality is\r\n" );
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document.write( "    |-4x| + |-5| ≤ 1.\r\n" );
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document.write( "Notice that  |-4x| = |4x|  and  |-5| = 5.  \r\n" );
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document.write( "Therefore, we can rewrite the starting inequality in this equivalent form\r\n" );
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document.write( "    |4x| + 5 <= 1\r\n" );
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document.write( "and then, subtracting 5 from both sides\r\n" );
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document.write( "    |4x| <= 1 - 5\r\n" );
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document.write( "    |4x| < -4.\r\n" );
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document.write( "But the number (absolute value) |4x| is always non-negative, so it can not be lesser than negative 4.\r\n" );
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document.write( "Hence, the original equation has no solution.\r\n" );
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document.write( "Exactly as it is stated in your textbook.\r\n" );
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document.write( "Solved and fully explained.\r<BR>\n" );
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