document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1144251>Question 1144251</A>: <I><SPAN STYLE=\"word-break: break-all;\"> five times the lesser of two consecutive even integers is at most four times the greatergreater.What are the possible values of the integers? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #765296 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=765296\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let the two consecutive even integers be equal to x and x + 2.<BR>\n" );
document.write( "your equation becomes 5x <= 4 * (x + 2)<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "5x <= 4x + 8<BR>\n" );
document.write( "solve for x to get:<BR>\n" );
document.write( "x <= 8\r<BR>\n" );
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document.write( "this means that x has to be either:<BR>\n" );
document.write( "8 or 6 or 4 or 2 or 0 or -2 or -4 .....\r<BR>\n" );
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document.write( "this also means that x cannot be greater than 8, which means that x cannot be either:<BR>\n" );
document.write( "10 or 12 or 12 or 16 or 18 .........\r<BR>\n" );
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document.write( "when x = 8, the equation becomes 5 * 8 <= 4 * 10 which becomes 40 <= 40 which is true.\r<BR>\n" );
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document.write( "when x = 6, which is smaller than 8, the equation becomes 5 * 6 <= 4 * 8 which becomes 30 <= 32 which is true.\r<BR>\n" );
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document.write( "when x = 10, which is greater than 8, the equation becomes 5 * 10 <= 4 * 12 which becomes 50 <= 48 which is false.\r<BR>\n" );
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document.write( "you can graph this by breaking it up into two equations as listed below.<BR>\n" );
document.write( "y = 5 * x<BR>\n" );
document.write( "y = 4 * (x + 2)\r<BR>\n" );
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document.write( "you graph both these equations on the same graph as shown below.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/082701.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "the red line is the graph of the equation y = 5x.<BR>\n" );
document.write( "the blue line is the graph of the equation y = 4 * (x + 2).\r<BR>\n" );
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document.write( "you can see that the red line is below the blue line up until the value of x is equal to 8, after which it is above the blue line.\r<BR>\n" );
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document.write( "this visually confirms the fact that 5x <= 4 * (x + 2) when the value of x is less than or equal to 8.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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