document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1023751>Question 1023751</A>: <I><SPAN STYLE=\"word-break: break-all;\"> simplify the expression shown 5x/2*1/x </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #639191 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=639191\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the car's value is 31,700.<BR>\n" );
document.write( "it depreciates 1,800 per year.<BR>\n" );
document.write( "in how many year will the value be 15,500.\r<BR>\n" );
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document.write( "for its value to be 15,500, it must have depreciated 31,700 - 15,500 = 16,200.\r<BR>\n" );
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document.write( "16,200 / 1,800 = 9\r<BR>\n" );
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document.write( "the car's value will be 15,500 in 9 years.\r<BR>\n" );
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document.write( "this can be modeled by a linear equation of y = -1,800 * x + 31,700.\r<BR>\n" );
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document.write( "graph the equation and find the intersection with the line of y = 15,500.\r<BR>\n" );
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document.write( "the graph is shown below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2016/030701.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "since this is linear, it can also be treated as an arithmetic progression.\r<BR>\n" );
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document.write( "the formula is An = A1 + (n-1) * d\r<BR>\n" );
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document.write( "A1 = 31,700<BR>\n" );
document.write( "d = 1,800<BR>\n" );
document.write( "An = 15,500\r<BR>\n" );
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document.write( "use the formula to solve for n.\r<BR>\n" );
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document.write( "you get 15,500 = 31,700 - (n-1) * 1,800\r<BR>\n" );
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document.write( "subtract 31,700 from both sides of the equation to get 15,500 - 31,700 = - (n-1) * 1,800.\r<BR>\n" );
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document.write( "combine like terms to get -16,200 = - (n-1) * 1,800.\r<BR>\n" );
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document.write( "divide both sides of the equation by 1,800 to get -16,200 / 1,800 = - (n-1)\r<BR>\n" );
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document.write( "simplify to get -9 = - (n-1)\r<BR>\n" );
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document.write( "remove parentheses to get -9 = -n + 1\r<BR>\n" );
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document.write( "subtract 1 from both sides of the equation to get -9 - 1 = -n\r<BR>\n" );
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document.write( "combine like terms to get -10 = -n \r<BR>\n" );
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document.write( "multiply both sides of the equation to get n = 10.\r<BR>\n" );
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document.write( "the tenth term in the progression is equal to 15,500.\r<BR>\n" );
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document.write( "since the progression starts at n = 1, then the tenth term is 9 years away from the first term.\r<BR>\n" );
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document.write( "the difference between the graphical solution and the arithmetic progression solution is that the graph starts at n = 0 and the arithmetic progression starts at n = 1.\r<BR>\n" );
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document.write( "that's why the tenth term in the arithmetic progression is equivalent to the ninth term in the graphical solution.\r<BR>\n" );
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document.write( "the algebraic solution and the graphical solution correspond.\r<BR>\n" );
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document.write( "the equation is y = 31,700 - 1,800 * x.\r<BR>\n" );
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document.write( "x is the number of years (same as n in the progression).\r<BR>\n" );
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document.write( "set y = 15,500 and the equation becomes 15,500 = 31,700 - 1,800 * x.\r<BR>\n" );
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document.write( "subtract 31,700 from both sides of the equation to get -16,200 = -1,800 * x.\r<BR>\n" );
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document.write( "divide both sides of the equaiton by 1,800 to get -9 = -x.\r<BR>\n" );
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document.write( "multiply both sides of the equation by -1 to get 9 = x which is the same as x = 9.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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