document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1012038>Question 1012038</A>: <I><SPAN STYLE=\"word-break: break-all;\"> [(X-4)/3]-[3/(X-4)]>(1/3)X </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #627885 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=627885\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> this inequality is true when x > 7/4 and x < 4.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this can also be expressed as x > 1.75 x < 4.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this can also be expressed as 1.75 < x < 4.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this can be seen easily in the following graph.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2016/010202.jpg\" alt=\"$$$\" </>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the equation is discontinuous at x = 4, and has a vertical asymptote at x = 4, as you can see on the graph.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "as the graph approaches x = 4 from the left, (x-4)/3 - (3/(x-4) approaches positive infinity.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "as the graph approaches x = 4 from the right, (x-4)/3 - (3/(x-4) approaches minus infinity.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "at x = 7/4 the graph of (x-4)/3 - (3/(x-4) is equal in value to the graph of x/3.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the graph helps you tremendously to see what is happening.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if you don't have a good graphing software available, then get one.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "it helps to visualize what is happening.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "otherwise, you're working blind unless you can construct a graph manually.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the one i used is at http://www.desmos.com/calculator.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "one of the ways you would solve this algebraically as follows:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "start with:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-4%29%2F3+-+3%2F%28x-4%29+%3E+x%2F3 ALIGN=MIDDLE  ALT=\"%28x-4%29%2F3+-+3%2F%28x-4%29+%3E+x%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "subtract x/3 from both sides of the equation to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-4%29%2F3+-+3%2F%28x-4%29+-+x%2F3+%3E+0 ALIGN=MIDDLE  ALT=\"%28x-4%29%2F3+-+3%2F%28x-4%29+-+x%2F3+%3E+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "set the equation equal to 0 to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-4%29%2F3+-+3%2F%28x-4%29+-+x%2F3+=+0 ALIGN=MIDDLE  ALT=\"%28x-4%29%2F3+-+3%2F%28x-4%29+-+x%2F3+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "solve for x to get x = 7/4.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "look at your equation to see that it has a vertical asymptote at x = 4.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you have 2 checkpoints.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you have y = 0 at x = 7/4 and you have y = undefined at x = 4.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the graph will be continuous up to x = 4 and will be continuous after x = 4.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you need to check 3 intervals.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the intervals are:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x < 7/4<BR>\n" );
document.write( "x > 7/4 and < 4<BR>\n" );
document.write( "x > 4\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "when x < 7/4, y is negative.<BR>\n" );
document.write( "when x > 7/4 and less than 4, y is positive.<BR>\n" );
document.write( "when x > 4, y is negative\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this means the graph is positive between x = 7/4 and x = 4 but not including x = 7/4 and x = 4.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that's your solution, because:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-4%29%2F3+-+3%2F%28x-4%29+%3E+x%2F3 ALIGN=MIDDLE  ALT=\"%28x-4%29%2F3+-+3%2F%28x-4%29+%3E+x%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-4%29%2F3+-+3%2F%28x-4%29+-+x%2F3+%3E+0 ALIGN=MIDDLE  ALT=\"%28x-4%29%2F3+-+3%2F%28x-4%29+-+x%2F3+%3E+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );