document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=776554>Question 776554</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I'm confused by the outcome I get from the problem 1/4|x-3|+2 <1 since < in the original equation is supposed to represent \"and\", yet my answer when graphed shows an \"or\" trend on my number line. When I solved it, I ended out with x <7 and x>-1. If you see anything I've done wrong, please correct me, and I thank you in advance for your input. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #473621 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=473621\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "Your problem is that you are ignoring the elephant in the living room. No matter what happens inside of the absolute value bars, the absolute value quantity will be greater than or equal to zero.  So the smallest value that <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{1}{4}|x\ -\ 3|\"> can assume is zero, namely when <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x = 3\">.  So when <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x\ =\ 3\">, the entire LHS of the inequality evaluates to 2 which is always larger than 1.  Hence, there are no real values of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x\"> that satisfy the given inequality.\r<BR>\n" );
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document.write( "So let's solve the thing and see if we get a result compatible with our intuition.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{1}{4}|x\ -\ 3|\ +\ 2\ <\ 1\">\r<BR>\n" );
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document.write( "Multiply by 4\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ |x\ -\ 3|\ +\ 8\ <\ 4\">\r<BR>\n" );
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document.write( "Add -8 to both sides:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ |x\ -\ 3|\ <\ -4\">\r<BR>\n" );
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document.write( "(((actually, we could have quit right here.  Right?)))\r<BR>\n" );
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document.write( "Then either\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x\ -\ 3\ <\ -4\ \Right\ x\ <\ -1\">\r<BR>\n" );
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document.write( "Or\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x\ -\ 3\ >\ 4\ \Right\ x\ >\ 7\">\r<BR>\n" );
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document.write( "You were correct in your assessment that the <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE <\"> in the original inequality indicated that you needed to find the intersection of two solution sets (\"and\" as you put it).  So, any value in the solution set of the original inequality must be simultaneously less than minus 1 and greater than 7.  Since there are no real numbers that fit these criteria, the solution set to the original inequality is indeed the null set.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "<font face=\"Math1\" size=\"+2\">Egw to Beta kai to Sigma</font><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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