document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=233186>Question 233186</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help solving this problem<BR>\n" );
document.write( "-5&#8804;2x+5 and 2x+5<9<BR>\n" );
document.write( "The solution is {X|&#9608;&#9608;&#8804;X<&#9608;&#9608;} </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #172122 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=172122\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> -5&#8804;2x+5 and 2x+5<9\r<BR>\n" );
document.write( "\n" );
document.write( "This is equivalent to:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-5 <= 2x+5 < 9\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "whatever you do to one side of the equation, you have to do to all the other sides.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "subtract 5 from all sides of the equation to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-5 -5 <= 2x + 5 - 5 < 9 - 5\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-10 <= 2x < 4\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "divide all sides of this equation by 2 to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-5 <= x < 2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "test in the original equation to see if the original equation holds true.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "take several values of x within the limits and outside of the limits.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "try x = -6, -5, 0, 1, 2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-6 and 2 are outside the limits.   -5, 0, 1 are within the limits.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "when x = -6, equation of -5 <= 2x+5 < 9 becomes:<BR>\n" );
document.write( "-5 <= -12 + 5 < 9 which becomes:<BR>\n" );
document.write( "-5 <= -7 < 9 which is NOT true because -5 is NOT <= -7<BR>\n" );
document.write( "this is ok because -6 was outside the limits.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "when x = -5, equation of -5 <= 2x+5 < 9 becomes:<BR>\n" );
document.write( "-5 <= -10 + 5 < 9 which becomes:<BR>\n" );
document.write( "-5 <= -5 < 9 which IS true.<BR>\n" );
document.write( "this is ok because -5 was within the limits.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "when x = 0, equation of -5 <= 2x+5 < 9 becomes:<BR>\n" );
document.write( "-5 <= 0 + 5 <= 9 which becomes:<BR>\n" );
document.write( "-5 <= 0 <= 9 which IS true.<BR>\n" );
document.write( "this is ok because 0 was within the limits.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "when x = 1, equation of -5 <= 2x+5 < 9 becomes:<BR>\n" );
document.write( "-5 <= 2 + 5 < 9 which becomes:<BR>\n" );
document.write( "-5 <= 7 < 9 which IS true.<BR>\n" );
document.write( "this is ok because 1 was within the limits.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "when x = 2, equation of -5 <= 2x+5 < 9 becomes:<BR>\n" );
document.write( "-5 <= 4 + 5 < 9 which becomes:<BR>\n" );
document.write( "-5 <= 9 < 9 which is NOT true because 9 is not < 9.<BR>\n" );
document.write( "this is ok because 2 was outside the limits.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "equation looks good and your answer is:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-5 <= x < 2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "which is the same as:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-5 <= x and x < 2.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this is also the same as:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x >= -5 and x < 2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you could also have done each of the inequalities separately and then combined them.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "your equation was:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-5 <= 2x + 5 and 2x+5 < 9\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "solve -5 <= 2x + 5 to get -5 <= x\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "solve 2x + 5 < 9 to get x < 2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-5 <= x and x < 2 is equivalent to -5 <= x < 9.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );