document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=406080>Question 406080</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi i have two questions, one dealing with inequalities. Im only in pre algebra and i dont understand. Can you please answer this and maybe i will understand? \r<BR>\n" );
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document.write( "Solve the following inequality:\r<BR>\n" );
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document.write( "2 < -8s\r<BR>\n" );
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document.write( "Now for the second question its a word problem having to do with feet per second? Another person asked this same math question, but the answer was wrong!\r<BR>\n" );
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document.write( "QUESTION : ACCORDING TO THE GUINNESS BOOK OF WORLD RECORDS, THE PEREGRINE FALCON HAS A RECORD DIVING SPEED OF 168 MILES PER HOUR. WRITE THIS SPEED PER SOCOND. \r<BR>\n" );
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document.write( "Thankyou! Please respond quick.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #286666 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=286666\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hi,\r<BR>\n" );
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document.write( "  I'll explain this problem with a more simple problem that shows<BR>\n" );
document.write( "the exact same idea.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+%3E+-x ALIGN=MIDDLE  ALT=\"1+%3E+-x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OK, what you want to find is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >. What is the given inequality telling you?<BR>\n" );
document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+1 ALIGN=MIDDLE  ALT=\"x+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+%3E+-1 ALIGN=MIDDLE  ALT=\"1+%3E+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > true<BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+0 ALIGN=MIDDLE  ALT=\"x+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+%3E0 ALIGN=MIDDLE  ALT=\"1+%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" > true<BR>\n" );
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document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-1 ALIGN=MIDDLE  ALT=\"x+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+%3E+1 ALIGN=MIDDLE  ALT=\"1+%3E+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > not true<BR>\n" );
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document.write( "In fact, if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > is -1, -2, -3, -4, or any minus number more negative than <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "the inequality is not true. It is true for any number that is more positive than <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "That includes the negative fractions like -1/3, -1/4, -1/5, etc. and also the <BR>\n" );
document.write( "positive fractions like 1/3, 1/4, etc. and then it is true for all the positive numbers,<BR>\n" );
document.write( "1, 2, 3, 4, etc.<BR>\n" );
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document.write( "Now I still want to find <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 normal way to do this with an equality is to<BR>\n" );
document.write( "divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28-1%29+%3E+%28-x%29%2F%28-1%29 ALIGN=MIDDLE  ALT=\"1%2F%28-1%29+%3E+%28-x%29%2F%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "plus divided by minus is minus and<BR>\n" );
document.write( "minus divided by minus is plus, so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1+%3E+x ALIGN=MIDDLE  ALT=\"-1+%3E+x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and now just write this going from right to left<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%3C+-1 ALIGN=MIDDLE  ALT=\"x+%3C+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > this is the same thing<BR>\n" );
document.write( "But what happened? I said the original inequality was true for all numbers<BR>\n" );
document.write( "greater than <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or, in other words, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%3E+-1 ALIGN=MIDDLE  ALT=\"x+%3E+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >. <BR>\n" );
document.write( "Now I divided both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and the result is telling me just the opposite.<BR>\n" );
document.write( "This leads to a general rule:<BR>\n" );
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document.write( "Whenever you divide both sides of an inequality by a minus quantity,  <BR>\n" );
document.write( "you must reverse the inequality sign when you are done.<BR>\n" );
document.write( "Following this law:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+%3E+-x ALIGN=MIDDLE  ALT=\"1+%3E+-x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28-1%29+%3C+%28-x%29%2F%28-1%29 ALIGN=MIDDLE  ALT=\"1%2F%28-1%29+%3C+%28-x%29%2F%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1+%3C+x ALIGN=MIDDLE  ALT=\"-1+%3C+x\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "Now rewriting this from right to left:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%3E+-1 ALIGN=MIDDLE  ALT=\"x+%3E+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Notice I reversed the inequality sign, and it is now true.<BR>\n" );
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document.write( "So, to solve your problem:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2+%3C+-8s ALIGN=MIDDLE  ALT=\"2+%3C+-8s\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F%28-1%29+%3E+%28-8%2F-1%29%2As ALIGN=MIDDLE  ALT=\"2%2F%28-1%29+%3E+%28-8%2F-1%29%2As\"   DISABLED_style= \"max-width:90%; height:auto;\" > (I reversed the inequality sign)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F4+%3E+s ALIGN=MIDDLE  ALT=\"-1%2F4+%3E+s\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s+%3C+-1%2F4 ALIGN=MIDDLE  ALT=\"s+%3C+-1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > (I just rewrote it going right to left)<BR>\n" );
document.write( "This is true- try any number that is greater than or equal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F4 ALIGN=MIDDLE  ALT=\"-1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "and the inequality becomes false.<BR>\n" );
document.write( "for example:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s+=+-1%2F10 ALIGN=MIDDLE  ALT=\"s+=+-1%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2+%3C+-8%2A%28-1%2F10%29 ALIGN=MIDDLE  ALT=\"2+%3C+-8%2A%28-1%2F10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20+%3C+8%2F10 ALIGN=MIDDLE  ALT=\"20+%3C+8%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" > not true<BR>\n" );
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document.write( "I hope all this helps and isn't too confusing.<BR>\n" );
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document.write( "  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );