document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=771585>Question 771585</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Jane is thinking of a number between -10 and 10.  If you multiply Jane’s number by -2, then subtract 2, the result is greater than 6.  Is Jane's number greater than -4 or less than -4? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #470364 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=470364\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The fact that the number is between -10 and 10 does not matter for the problem.<BR>\n" );
document.write( "However, if you had to guess the number, knowing that it is between -10 and 10 would improve your chances.<BR>\n" );
document.write( " <BR>\n" );
document.write( "THE GUESSER SOLUTION:<BR>\n" );
document.write( "Could it be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >?<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%2A0-2=0-2=-2 ALIGN=MIDDLE  ALT=\"-2%2A0-2=0-2=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and that is not greater than 6, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" > cannot be Jane's number.<BR>\n" );
document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" > is  greater than -4, and it does not work, the solution must be that<BR>\n" );
document.write( "Jane's number is less than -4<BR>\n" );
document.write( " <BR>\n" );
document.write( "THE ALGEBRA SOLUTION:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >= the number Jane is thinking<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2x ALIGN=MIDDLE  ALT=\"-2x\"   DISABLED_style= \"max-width:90%; height:auto;\" >= the number Jane is thinking multiplied times <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2 ALIGN=MIDDLE  ALT=\"-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2x-2 ALIGN=MIDDLE  ALT=\"-2x-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >= the result of multiplying Jane's number times -2, and then subtracting 2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2x-2%3E6 ALIGN=MIDDLE  ALT=\"-2x-2%3E6\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%28x%2B1%29%3E6 ALIGN=MIDDLE  ALT=\"-2%28x%2B1%29%3E6\"   DISABLED_style= \"max-width:90%; height:auto;\" > (taking out the common factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2 ALIGN=MIDDLE  ALT=\"-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%28x%2B1%29%3E6 ALIGN=MIDDLE  ALT=\"-2%28x%2B1%29%3E6\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%28x%2B1%29%2F%28-2%29%3C6%2F%28-2%29 ALIGN=MIDDLE  ALT=\"-2%28x%2B1%29%2F%28-2%29%3C6%2F%28-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (because on multiplying/dividing by a negative number we are flipping around the number line, and that flips the inequality sign, see NOTE below)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%28x%2B1%29%2F%28-2%29%3C6%2F%28-2%29 ALIGN=MIDDLE  ALT=\"-2%28x%2B1%29%2F%28-2%29%3C6%2F%28-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B1%3C-3 ALIGN=MIDDLE  ALT=\"x%2B1%3C-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > (just simplifying)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B1%3C-3 ALIGN=MIDDLE  ALT=\"x%2B1%3C-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >  --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B1-1%3C-3-1 ALIGN=MIDDLE  ALT=\"x%2B1-1%3C-3-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >  --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x%3C-4%29 ALIGN=MIDDLE  ALT=\"highlight%28x%3C-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (subtracting 1 from both sides and simplifying)<BR>\n" );
document.write( "So Jane's number is less than -4.<BR>\n" );
document.write( " <BR>\n" );
document.write( "NOTE:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=number_line%28+600%2C+-10%2C+10%2C+-4%2C+-6%2C+-8%2C+5+%29 ALIGN=MIDDLE  ALT=\"number_line%28+600%2C+-10%2C+10%2C+-4%2C+-6%2C+-8%2C+5+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8%3C-6%3C-4%3C5 ALIGN=MIDDLE  ALT=\"-8%3C-6%3C-4%3C5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The numbers to the left (of -4, or of any other number) are less, and the numbers to the right are more.<BR>\n" );
document.write( "Multiplying times -1 means changing the signs off all the numbers, so we end up with<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=number_line%28+600%2C+-10%2C+10%2C+4%2C+6%2C+8%2C+-5+%29 ALIGN=MIDDLE  ALT=\"number_line%28+600%2C+-10%2C+10%2C+4%2C+6%2C+8%2C+-5+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5%3C4%3C6%3C8 ALIGN=MIDDLE  ALT=\"-5%3C4%3C6%3C8\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%3E6%3E4%3E-5 ALIGN=MIDDLE  ALT=\"8%3E6%3E4%3E-5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "If one number was less than (to the left of) a certain number, after multiplying both numbers times -1, the order is reversed, so the signs change from < to > and from > to <. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );