document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=206915>Question 206915</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Graph the system of inequalities:<BR>\n" );
document.write( "y>or=x<BR>\n" );
document.write( "x<3<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 #156418 by </B><A HREF=/tutors/aboutme.mpl?userid=dlam5><B>dlam5(15)</B></A><img src=\"/images/stars/stars-06.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=dlam5><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=156418\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C200%2C+-10%2C+10%2C+-10%2C+10%2C+x%3C3%2C+y%3E=x%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C200%2C+-10%2C+10%2C+-10%2C+10%2C+x%3C3%2C+y%3E=x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "There is the graph.  But let's solve this LOGICALLY.\r<BR>\n" );
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document.write( "What I usually do is I forget about the inequality notations/signs, and say to myself: \"what would this graph look like NORMALLY, when x=3, or y=x?\"  \r<BR>\n" );
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document.write( "Well, then I know for a fact that y=x just comes down on the graph SLANTED.  Well, what does that mean?  WHERE does it slant?\r<BR>\n" );
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document.write( "Plug in values for x and y to find out.  \r<BR>\n" );
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document.write( "if...\r<BR>\n" );
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document.write( "x=1, y=1  \r<BR>\n" );
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document.write( "The ordered pair (1,1) comes out.\r<BR>\n" );
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document.write( "if...\r<BR>\n" );
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document.write( "x=-5, then y=-5\r<BR>\n" );
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document.write( "The ordered pair (-5,-5) comes out.\r<BR>\n" );
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document.write( "I usually pick up to 5 VALUES of ordered pairs, then just play connect the dots.  Now I know where it slants!  (see graph)\r<BR>\n" );
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document.write( "Let's try x<3.  Well, what does it look like if x = 3?  I now find out 3 is a CONSTANT, so when graphed, I go right (because, 3 is positive) 3 on the x axis, and get a straight line, vertical..\r<BR>\n" );
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document.write( "Because, x = 3, x IS 3, so 3 right is a vertical line!\r<BR>\n" );
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document.write( "As I add the inequalities in, this tells me where the ordered pairs are okay to be (viable).  \r<BR>\n" );
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document.write( "Well, how do I know where to shade?  Pick a point not on the line for each equation.\r<BR>\n" );
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document.write( "y>or=x;\r<BR>\n" );
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document.write( "I'll pick 9,2 for example.  This point (9,2) is NOT on the line.\r<BR>\n" );
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document.write( "9 is x; 2 is y.\r<BR>\n" );
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document.write( "is 2>or=9;  NO!  So, if 9,2 is close to the RIGHT of the graph, I SHADE opposite.  Because all of that AREA isn't true.  I shade to the left, as depicted on the graph.\r<BR>\n" );
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document.write( "Now, x<3.  This is an easy one.  It is saying \"the x-values (x's) are LESS THAN (smaller) 3, so smaller values of three are to the LEFT; and we shade left, as depicted on the graph.\r<BR>\n" );
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document.write( "And that's it.\r<BR>\n" );
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document.write( "e-mail for more help!\r<BR>\n" );
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document.write( "Thanks :)\r<BR>\n" );
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