document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=51817>Question 51817</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0395937787/algebrahomeworkh>algebra 2 equations, graohs, and applicatiopns</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> i have no idea how to graph  a linear inequality, could you please help me solve this problem step by step!!\r<BR>\n" );
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document.write( "x+y> or equal to -2<BR>\n" );
document.write( "-4x+y< or equal to -5\r<BR>\n" );
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document.write( "i dont know how to graph shade or plot the numbers could you please help me!!<BR>\n" );
document.write( "thanks!!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #34616 by </B><A HREF=/tutors/aboutme.mpl?userid=venugopalramana><B>venugopalramana(3286)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=venugopalramana><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.geocities.com/venugopalramana/FREE_MATHS_ASSISTANCE.html valign=middle><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=34616\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> see the following example and try<BR>\n" );
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document.write( "2x+y>=2..................1<BR>\n" );
document.write( "y<x.....................2<BR>\n" );
document.write( "y>0............................3<BR>\n" );
document.write( "step1.<BR>\n" );
document.write( "first write them as eqns. and plot as a normal graph....<BR>\n" );
document.write( "2x+y=2.....find points on the graph by taking any value for x and finding y from the given eqn.as shown below..<BR>\n" );
document.write( "x..............0.................1........................2.....etc<BR>\n" );
document.write( "y=2-2x......2.................0.......................-2......etc<BR>\n" );
document.write( "plot the graph of this eqn.it will be a straight line with slope of -2,and intercept of 2. <BR>\n" );
document.write( "y-x=0<BR>\n" );
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document.write( "x...........0................1....................2..........etc.<BR>\n" );
document.write( "y=x........o................1....................2.........etc...<BR>\n" );
document.write( "this graph is also a straight line through origin and slope of 1.<BR>\n" );
document.write( "y=0<BR>\n" );
document.write( "x.....................0............1..........................2..........etc<BR>\n" );
document.write( "y=0.................0.............0..........................0........etc<BR>\n" );
document.write( "this is also a straight line through origin ..in fact it is x axis.<BR>\n" );
document.write( "step 2.<BR>\n" );
document.write( "now detemine and shade / hatch the zone of required inequality..<BR>\n" );
document.write( "in the first case we want 2x+y>=2...we plotted 2x+y=2..so we take origin and test for the inequality..origin is x=0,y=0<BR>\n" );
document.write( "hence 2x+y=0+0=0 ..it is not greater than or equal to 2 .so the zone to be shaded is the area away from origin with the line considered as boundary,since area towards origin (as we have tested ) gives 2x+y<=0.so shade or hatch this area which you find is area above the line and includes the line as = is also allowed . <BR>\n" );
document.write( "do same way for the other 2 eqns...<BR>\n" );
document.write( "y-x  < 0 ....here it is the area below the line,and excludes the line since = is not mentioned.<BR>\n" );
document.write( "y>0.....here it is the area above x axis and excludes the line (x axis) since = is not mentioned.<BR>\n" );
document.write( "the common area belonging to all the 3 in the shaded zones is the required answer.it is the area above x axis,below y=x line and above 2x+y=0 line.see graph below..<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+500%2C+500%2C+-5%2C+10%2C+-5%2C+10%2C2-2%2Ax%2Cx%2C0+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+500%2C+500%2C+-5%2C+10%2C+-5%2C+10%2C2-2%2Ax%2Cx%2C0+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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