document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=856299>Question 856299</A>: <I><SPAN STYLE=\"word-break: break-all;\"> At George’s Graphics and More, the average<BR>\n" );
document.write( "starting salary for a new employee is<BR>\n" );
document.write( "$57,600, but the actual salary could differ from<BR>\n" );
document.write( "the average by as much $3590. Write an<BR>\n" );
document.write( "absolute value inequality to describe this<BR>\n" );
document.write( "situation. Solve it. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #515857 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=515857\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let x the actual salary.<BR>\n" );
document.write( "you get 2 equations.<BR>\n" );
document.write( "57600 - x <= 3590<BR>\n" );
document.write( "57600 - x >= -3590<BR>\n" );
document.write( "this fits the definition of absolute value which says that:<BR>\n" );
document.write( "|a| <= b if and only if a <= b and a >= -b<BR>\n" );
document.write( "in this problem:<BR>\n" );
document.write( "a = (57600 - x)<BR>\n" );
document.write( "b = 3590<BR>\n" );
document.write( "a <= b becomes (57600 - x) <= 3590<BR>\n" );
document.write( "a >= -b becomes (57600 - x) >= -3590<BR>\n" );
document.write( "the absolute value equation becomes:<BR>\n" );
document.write( "|57600 - x| <= 3590\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if you solve for this absolute value equation, you will find that:<BR>\n" );
document.write( "(57600 - x) <= 3590 and (57600 - x) >= -3590.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if you solve for x in each of these equations, you will get:<BR>\n" );
document.write( "x >= 54010 and x <= 61190\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this equation can also be written as:<BR>\n" );
document.write( "54010 <= x <= 61190.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x can be any value between 54010 and 61190.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you can graph this function as follows:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "graph y = |57600 - x|<BR>\n" );
document.write( "graph y = 3590\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the values for the graph of y = |57600 - x| have to be underneath the graph of y = 3590.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the graph was difficult to show, but i figured it out and it is shown below.<BR>\n" );
document.write( "the scale of the map is in thousands.<BR>\n" );
document.write( "57600 would be shown as 57.6<BR>\n" );
document.write( "3590 would be shown as 3.59\r<BR>\n" );
document.write( "\n" );
document.write( "because of this scale change, the equations that are graphed are:<BR>\n" );
document.write( "y = |57.6 - x|<BR>\n" );
document.write( "y = 3.59\r<BR>\n" );
document.write( "\n" );
document.write( "the value of y = |57.6-x| is smaller than y = 3.59 when x is greater than (57.6 - 3.59) and x is smaller than (57.6 + 3.59).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that makes x greater than or equal 54.01 and x smaller than or equal to 61.19 on the graph.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "in real life this means that the value of |57600 - x| <= 3590 when x is greater than or equal to 54010 and smaller than or equal to 61190.<BR>\n" );
document.write( "this is consistent with what was derived earlier.<BR>\n" );
document.write( "the graph supports it.<BR>\n" );
document.write( "the only difference is the change of scale in order to make the graph more legible.\r<BR>\n" );
document.write( "\n" );
document.write( " <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-5%2C70%2C-1%2C5%2Cabs%2857.6-x%29%2C3.59%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C-5%2C70%2C-1%2C5%2Cabs%2857.6-x%29%2C3.59%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\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( "<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" );