document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=78778>Question 78778</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how do i graph these conjunctions?\r<BR>\n" );
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document.write( "-3 < x and c < 0\r<BR>\n" );
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document.write( "-4 < x < -1\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 #56522 by </B><A HREF=/tutors/aboutme.mpl?userid=mathdoc314><B>mathdoc314(58)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mathdoc314><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=56522\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The first question looks weird to me.\r<BR>\n" );
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document.write( "You asked:  -3 < x and c < 0\r<BR>\n" );
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document.write( "You might have meant:  -3 < x and x < 0\r<BR>\n" );
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document.write( "To graph this you make a number line and color in the numbers that are<BR>\n" );
document.write( "between -3 and 0.  You make an open circle at the two endpoints -3 and 0<BR>\n" );
document.write( "to show they are not included in the set you are graphing.  (That is the<BR>\n" );
document.write( "set of all numbers that are greater than -3 and less than 0).  So it<BR>\n" );
document.write( "might look something like this\r<BR>\n" );
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document.write( " -5   -4  -3  -2  -1  0   1   2  \r\n" );
document.write( "  |---|---O///|///|///O---|---|\r\n" );
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document.write( "I used O for a round circle and //// to show it is shaded.\r<BR>\n" );
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document.write( "If you had something different, like -3 <= x and x <= 0, then<BR>\n" );
document.write( "the round circle would be filled in solid.  But since it is<BR>\n" );
document.write( "-3 < x and x < 0  then the endpoints are not shaded so the<BR>\n" );
document.write( "circles are left open, unfilled.\r<BR>\n" );
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document.write( "There is another interpretation where you meant something more like:<BR>\n" );
document.write( " -3 < x and y < 0<BR>\n" );
document.write( "where x and y would be two different variables.  However 'c' is usually used for a constant, and I am guessing you did not mean to graph this with two different variables.\r<BR>\n" );
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document.write( "The second one you do just about the same thing.  <BR>\n" );
document.write( "It says -4 < x < -1 which means the same as<BR>\n" );
document.write( "-4 < x and x < -1 .   (Something totally different is<BR>\n" );
document.write( "-4 < x OR x < -1, and that disjuction is the same as the<BR>\n" );
document.write( "second condition, x < -1,<BR>\n" );
document.write( "because it is true whenever the first condition is true.)\r<BR>\n" );
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document.write( "I hope that is enough of explanation for you\r<BR>\n" );
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