document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=405570>Question 405570</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello. I am having such a hard time understanding how to graph linear inequalities, from solving the problem to understanding where the points go on the x and y axis, if the line should be solid or dashed. I just can't make it click in my brain. Can you possibly show a very blunt breakdown of the following two equations? If I can follow it step by step I should be able to get it. Thank you so much!\r<BR>\n" );
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document.write( "1.) Graph 2x + y < 4\r<BR>\n" );
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document.write( "2.) Graph 4x - 3y >= 12 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #286455 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=286455\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1.) Graph 2x + y < 4<BR>\n" );
document.write( "Solve for \"y\":<BR>\n" );
document.write( "y < -2x+4<BR>\n" );
document.write( "----<BR>\n" );
document.write( "You NEVER graph an inequality directly.<BR>\n" );
document.write( "You graph its boundary which is always an equality.<BR>\n" );
document.write( "Graph y = -2x+4 as a dashed line because equality<BR>\n" );
document.write( "is not part of your problem.<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Plot: (0,4) and (1,2) and draw a dashed line thru them<BR>\n" );
document.write( "----<BR>\n" );
document.write( "Since you want y LESS than the boundary, shade <BR>\n" );
document.write( "the half-plane BELOW the boundary to get the graph<BR>\n" );
document.write( "of the inequality:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C300%2C-10%2C10%2C-10%2C10%2Cy+%3C+-2x%2B4%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C300%2C-10%2C10%2C-10%2C10%2Cy+%3C+-2x%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "====================\r<BR>\n" );
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document.write( "2.) Graph 4x - 3y >= 12<BR>\n" );
document.write( "Solve for \"y\":<BR>\n" );
document.write( "3y <= 4x-12<BR>\n" );
document.write( "y <= (4x-12)/3<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Now graph the boundary as a solid<BR>\n" );
document.write( "line because it is part of the problem<BR>\n" );
document.write( "Plot (0,-4)(2,-4/3)<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Shade the half-plane BELOW the boundary<BR>\n" );
document.write( "because you want y LESS than the boundary.<BR>\n" );
document.write( "The line and the shaded area are the graph.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C300%2C-10%2C10%2C-10%2C10%2C%284x-12%29%2F3%2Cy%3C%284x-12%29%2F3%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C300%2C-10%2C10%2C-10%2C10%2C%284x-12%29%2F3%2Cy%3C%284x-12%29%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=============================================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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