document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=208439>Question 208439</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 20-4 over 5x is greater then or equal to 16?<BR>\n" );
document.write( "greater then=> (if i have it wrong, its less then) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #157657 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=157657\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you manipulate inequalities much the same way you manipulate equalities.<BR>\n" );
document.write( "the only real difference is that if you multiply both sides of an inequality by -1 then you reverse the inequality.<BR>\n" );
document.write( "example:<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "equality:<BR>\n" );
document.write( "a = b<BR>\n" );
document.write( "multiply both sides by -1 to get:<BR>\n" );
document.write( "-a = -b<BR>\n" );
document.write( "the signs are reversed and the equality is preserved.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "inequality:<BR>\n" );
document.write( "a > b<BR>\n" );
document.write( "multiply both sides by -1 to get:<BR>\n" );
document.write( "-a < -b<BR>\n" );
document.write( "the signs are reversed and the inequality is reversed.  where it said > now it says <.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "your equation looks like this:<BR>\n" );
document.write( "(20-4)/5x >= 16<BR>\n" );
document.write( "as far as i can tell.<BR>\n" );
document.write( "to solve this you do the following:<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "multiply both sides by x to bring the x over to the right side of the equation and remove it from the denominator.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "you get:<BR>\n" );
document.write( "(20-4)/5 >= 16 * x<BR>\n" );
document.write( "which becomes:<BR>\n" );
document.write( "16/5 >= 16x<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "divide both sides by 16 to get:<BR>\n" );
document.write( "16/(16*5) >= x<BR>\n" );
document.write( "this becomes:<BR>\n" );
document.write( "1/5 >= x<BR>\n" );
document.write( "to get x over to the left side of this equation you have to subtract x from both sides of this equation and to get 1/5 over to the right side of this equation you have to subtract 1/5 from both sides of this equation.<BR>\n" );
document.write( "you get:<BR>\n" );
document.write( "-x >= - (1/5)<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "here's where the reversal of signs comes in.<BR>\n" );
document.write( "if you multiply both sides of this equation by (-1) you get:<BR>\n" );
document.write( "x <= (1/5)<BR>\n" );
document.write( "note the inequality was reversed.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "the answer to this question is that if x <= 1/5, then the original equation of 16/5x >= 16 holds true, assuming i interpreted the original equation correctly.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "if x = 1/5 = .2, this equation becomes 16/1 >= 16 which is true.<BR>\n" );
document.write( "if x = .3, this equation becomes 16/1.5 >= 16 which is false.<BR>\n" );
document.write( "if x = .1, this equation becomes 16/.5 >= 16 which is true.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "answer is x <= (1/5)<BR>\n" );
document.write( "-----\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );