document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=340854>Question 340854</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sum of two numbers is greater than or equal to 14  . The second number is 2 less than the first. What are the possible values for the first of the two numbers? <BR>\n" );
document.write( "In your answer, denote the first number by x.\r<BR>\n" );
document.write( "\n" );
document.write( "The sum of two numbers is less than or equal to28  . The second number is 8 more than the first. What are the possible values for the first of the two numbers? <BR>\n" );
document.write( "In your answer, denote the first number by x  \r<BR>\n" );
document.write( "\n" );
document.write( "Thank whoever help me I need these two answers badly.  Thank you again! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #244151 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=244151\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> first problem:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x + y >= 14<BR>\n" );
document.write( "y = x - 2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Substitute x-2 for y in the first equation to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x + x - 2 >= 14\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Solve for x to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x >= 8\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "You do this by adding 2 to both sides of the equation and then combining terms on each side of the equation and then dividing both sides of the equation by 2.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Since y = x - 2, then y will always be 2 less than whatever x is.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Confirm by substituting for x and y in the original equation.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "If x is greater than or equal to 8, the equation should be true, and if x is smaller than 8, the equation should be false.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Examples:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "When x = 8, then y = 6, and x + y >= 14 becomes 14 >= 14 which is true.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "When x = 6, then y = 4, and x + y >= 14 becomes 10 >= 14 which is false.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "When x = 10, then y = 8, and x + y >= 14 becomes 18 >= 14 which is true.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "second problem:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x + y <= 28<BR>\n" );
document.write( "y = x + 8\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Substitute x + 8 for y in the first equation to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x + x + 8 <= 28\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Solve for x to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x <= 10\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "You do this by subtracting 8 from both sides of the equation and then combining like terms and then dividing both sides of the equation by 2.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Since y = x + 8, then y will always be 8 more than whatever x is.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Confirm by substituting for x and y in the original equation.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "If x is smaller than or equal to 10, then the equation should be true.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "If x is greater than 10, then he equation should be false.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Example:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "When x = 10, y = 18, and x + y <= 28 becomes 28 <= 28 which is true.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "When x = 12, y = 20, and x + y <= 28 becomes 32 <= 28 which is false.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "When x = 8, y = 16, and x + y <= 28 becomes 24 <= 28 which is true.\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );