document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1107610>Question 1107610</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help. I'm trying to solve and graph the inequality.\r<BR>\n" );
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document.write( "I'm confused on it because the b is negative. I don't think it can be graphed. Here's what I have. Can you please tell me if I'm correct. \r<BR>\n" );
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document.write( "-8-b less than equal to -8<BR>\n" );
document.write( "-8+8-b less than equal to -8+8<BR>\n" );
document.write( "-b less than equal to 0\r<BR>\n" );
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document.write( "Thank you.<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 #722620 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=722620\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> your equation is -8 - b <= -8<BR>\n" );
document.write( "as you did, add 8 to both sides of the equation to get -8 + 8 - b <= -8 + 8.<BR>\n" );
document.write( "simplify to get -b <= 8.\r<BR>\n" );
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document.write( "to solve for b, multiply both sides of this equation by -1 to get b >= -8\r<BR>\n" );
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document.write( "you have to remember that, when you multiply or divide both sides of an inequality by a negative numer, the inequality reverses.\r<BR>\n" );
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document.write( "here's a couple of examples;\r<BR>\n" );
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document.write( "5 < 8<BR>\n" );
document.write( "multiply both sides by -1 and you get -5 > -8.<BR>\n" );
document.write( "multiply both sides by -2 and you get -10 > -16.\r<BR>\n" );
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document.write( "divide both sides of -10 > -16 by -2 and you get 5 < 8.\r<BR>\n" );
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document.write( "your solution is -b <= 0 which is the same as b >= 0.\r<BR>\n" );
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document.write( "to graph this, let x = b and the equation becomes x >= 0.\r<BR>\n" );
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document.write( "you would draw the line x = 0 on the graph and then shade the area of the graph that is to the right of x = 0.\r<BR>\n" );
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document.write( "your graph would look like this.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2018/012602.jpg\" alt=\"$$$\">\r<BR>\n" );
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document.write( "to see if your solution is corect, go back to the original equation and check to see if the equation is true when b is >= 0 and not true when b is < 0.\r<BR>\n" );
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document.write( "your original equation is -8 - b <= -8\r<BR>\n" );
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document.write( "when b = 0, this equation becomes -8 <= -8 which is true.\r<BR>\n" );
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document.write( "when b is less than 0, like say -1, this equation becomes -8 -(-1) <= -8.\r<BR>\n" );
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document.write( "this simplifies to -8 + 1 <= -8 which becomes -7 <= -8 which is false.\r<BR>\n" );
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document.write( "when b is greater than 0, like say 1, this equation becomes -8 - 1 <= -8.\r<BR>\n" );
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document.write( "this simplifies to -9 <= -8 which is true.\r<BR>\n" );
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document.write( "the inequality is true when b is greater than or equal to 0.\r<BR>\n" );
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document.write( "the inequality is false when b is less than 0.\r<BR>\n" );
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document.write( "when your variable of interest is negative, multiply both sides of the inequality or the equation by -1 to make it positive.\r<BR>\n" );
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document.write( "with an equation, the equality will still hold.\r<BR>\n" );
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document.write( "with an inequality, the inequality reverses.\r<BR>\n" );
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document.write( "if -x = y, then x = -y.\r<BR>\n" );
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document.write( "if -x >= y, then x <= -y.\r<BR>\n" );
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document.write( "if -x > y, then x < -y.\r<BR>\n" );
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document.write( "if -x <= y, then x >= -y.\r<BR>\n" );
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document.write( "if -x < y, then x > -y.\r<BR>\n" );
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