document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=421215>Question 421215</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi! I would really appreciate some help solving these problems. \"Graph the solution set of the following linear inequality 2(y+3)< -x? There is also this one I am stumped on as well, -7y-8x(is greater than or equal to)-7y+56? I know what type of line they are asking for, Dotted or solid, but when it comes to answering what points they want me to plot I am lost.<BR>\n" );
document.write( "Thank you in advance for taking the time to answer =) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #294184 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=294184\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> in order to graph the solution, you have to solve for y.\r<BR>\n" );
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document.write( "for example:\r<BR>\n" );
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document.write( "your first equation is 2 * (y+3) < -x\r<BR>\n" );
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document.write( "divide both sides of the equation by 2 to get:\r<BR>\n" );
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document.write( "y + 3 < -x/2\r<BR>\n" );
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document.write( "subtract 3 from both sides of the equation to get:\r<BR>\n" );
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document.write( "y < -x/2 - 3\r<BR>\n" );
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document.write( "now you can graph the equation.\r<BR>\n" );
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document.write( "to graph it, set the equation to an equality rather than an inequality.\r<BR>\n" );
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document.write( "you will graph y = -x/2 - 3\r<BR>\n" );
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document.write( "graph of that equation is shown below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-10%2C10%2C-10%2C10%2C-x%2F2+-+3%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C-10%2C10%2C-10%2C10%2C-x%2F2+-+3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "since your inequality states that y < -x/2 - 3, than any value of y that is in the area underneath the line y = -x/2 - 3 will satisfy the equation.\r<BR>\n" );
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document.write( "for example:\r<BR>\n" );
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document.write( "when x = 2, y = -2/2 - 3 = -1 - 3 = -4\r<BR>\n" );
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document.write( "when x = 2, any value of y < -4 will satisfy the equation of y < -x/2 - 3.\r<BR>\n" );
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document.write( "by shading the area underneath the line of the equation, you indicate the possible values that y can take that satisfy the equation y < -x/2 - 3.\r<BR>\n" );
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document.write( "not that y < -4 will satisfy the equation when x = 2, but will not satisfy the equation when x = 4.\r<BR>\n" );
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document.write( "when x = 4, the line of the equation is equal to -4/2 - 3 = -2 - 3 = -5.\r<BR>\n" );
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document.write( "when x = 4, y needs to be less than -5 to satisfy the equation.\r<BR>\n" );
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document.write( "i redrew the equation of the line y = -x/2 - 3 and added lines at y = -4 and y = -5 so you can see that more clearly.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-10%2C10%2C-10%2C10%2C-x%2F2+-+3%2C-4%2C-5%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C-10%2C10%2C-10%2C10%2C-x%2F2+-+3%2C-4%2C-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "bottom line:\r<BR>\n" );
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document.write( "you solve for y so you can graph the inequality.<BR>\n" );
document.write( "you graph the equality.<BR>\n" );
document.write( "you shade the area that supports the inequality.\r<BR>\n" );
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document.write( "in this case, the shaded area would be underneath the line because the inequality indicates less than. </SPAN>\n" );
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