document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1046917>Question 1046917</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the inequalities by graphing\r<BR>\n" );
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document.write( "y<=4x-1<BR>\n" );
document.write( "y>3x-1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #662487 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=662487\">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%2C300%2C-2%2C2%2C-2%2C2%2C4x-1%2C3x-1%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-2%2C2%2C-2%2C2%2C4x-1%2C3x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You find which side the inequality holds by setting x and y equal to 0.  If the inequality is true, that entire side of the line that contains the origin is true..<BR>\n" );
document.write( "For the first graph, the one tilted less from the vertical (steeper), it is the area below or to the right of that line. At the origin, 0<=-1, and that is not true, so the other side of the line has the inequality work.<BR>\n" );
document.write( "For the second graph, less steep, at the origin, 0>-1, and that is true, so the side of the line containing the origin is true. <BR>\n" );
document.write( "Where both halves overlap, the inequality is solved.  That would be to the left of the green line and to the right of the red line, or where x>0.<BR>\n" );
document.write( "That occurs in the thin strip that begins at (0,-1). The point itself is not part of the overlap, because y>3x-1, not greater than or equal to.  <BR>\n" );
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document.write( "For any positive x, this works.  x=1/2 and y<=1, and y >0.5<BR>\n" );
document.write( "For x=3, y<=11 and y>8<BR>\n" );
document.write( "Negative x should not work.<BR>\n" );
document.write( "Pick x=-1/2<BR>\n" );
document.write( "y<=-3<BR>\n" );
document.write( "y>-2.5  There is no solution here </SPAN>\n" );
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