document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1123449>Question 1123449</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The balance of a loan is $2,570 in January, and the monthly payment is $125.50. The relationship between the loan balance, y, and the number of monthly payments made since January, x, can be represented by the equation y = 2,570 - 125.50x. In what months does the loan balance, y, meet the condition, $1,600 < y < $2,000? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #739760 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=739760\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> your equation is y = 2570 - 125.5 * x\r<BR>\n" );
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document.write( "you want to know when 1600 < y < 2000\r<BR>\n" );
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document.write( "since y = 2570 - 125.5 * x, then you can replace y with 2570 - 125.5 * x and you then want to know when 1600 < 2570 - 125.5 * x < 2000\r<BR>\n" );
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document.write( "subtract 2570 from all sides of this inequality to get:\r<BR>\n" );
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document.write( "1600 - 2570 < -125.5 * x < 2570 - 2000\r<BR>\n" );
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document.write( "multiply all sides of this inequality by -1 to get:\r<BR>\n" );
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document.write( "-(1600 - 2570 > 125.5 * x > -(2570 - 2000)\r<BR>\n" );
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document.write( "simplify to get 970 > 125.5 * x > 570\r<BR>\n" );
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document.write( "divide all sides of this inequality by 125.5 to get 970 / 125.5 > x > 570 / 125.5\r<BR>\n" );
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document.write( "simplify to get 7.729083665 > x > 4.541832669\r<BR>\n" );
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document.write( "your answer will be somewhere between 4 and 8.\r<BR>\n" );
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document.write( "when x = 4, y = 2570 - 125.5 * x = 2068<BR>\n" );
document.write( "when x = 5, y = 2570 - 125.5 * x = 1942.5 which is < 2000\r<BR>\n" );
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document.write( "when x = 8, y = 2570 - 125.5 * x = 1566<BR>\n" );
document.write( "when x = 7, y = 2570 - 125.5 * x = 1691.5 which is > 1600\r<BR>\n" );
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document.write( "your answer is that 1600 < y < 2000 when x = 5 to 7.\r<BR>\n" );
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document.write( "you could have analyzed this from the answer of  7.729083665 > x > 4.541832669\r<BR>\n" );
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document.write( "if x > 4.541832669, then x > 4 which means x >= 5.\r<BR>\n" );
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document.write( "if x < 7.729083665, then x < 8 which means x <= 7.\r<BR>\n" );
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document.write( "x >= 5 and x <= 7 gets you x = 5 or 6 or 7, as long as x has to be an integer.\r<BR>\n" );
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document.write( "if you're in doubt, then doing it the way i did it above by checking x = 7,8,4,5 is a good way to be sure you got it right.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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