document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=571856>Question 571856</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find four consecutive even integers such that 4 times the sum of the first and fourth is 8 greater than 12 times the third. I have no idea how to do this problem. Someone explain it to me please? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #368676 by </B><A HREF=/tutors/aboutme.mpl?userid=mathsmiles><B>mathsmiles(68)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mathsmiles><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=mathsmiles><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=368676\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> So we're looking for 4 numbers.  Let's make the first number X.  (This is algebra, right?)\r<BR>\n" );
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document.write( "Since they're asking for even integers, the next number is X+2.  Make sense?<BR>\n" );
document.write( "The 3rd number is X+4.<BR>\n" );
document.write( "The 4th number is X+6.\r<BR>\n" );
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document.write( "Next they say if we add the first and 4th  and then multiply by 4 ... <BR>\n" );
document.write( "4[(X) + (X+6)] <BR>\n" );
document.write( "The results will be 8 more than 12 times the 3rd<BR>\n" );
document.write( "So the other side of the equation is 12(X+4) but we need to add 8 to equal the first side since we know the first side is 8 more than this.<BR>\n" );
document.write( "8+12(X+4)\r<BR>\n" );
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document.write( "Putting these together:<BR>\n" );
document.write( "4[X + (X + 6)] = 8 + 12(X + 4)  Now combine like terms on the left:<BR>\n" );
document.write( "4(2X + 6) = 8 + 12(X + 4)  Now multiplying the paren on the right<BR>\n" );
document.write( "4(2X + 6) = 8 + 12X + 48  Combining terms on the right:<BR>\n" );
document.write( "4(2X + 6) = 12X + 56  Multiplying the remaining paren on the left:<BR>\n" );
document.write( "8X + 24 = 12X + 56  Subtract 8X from both sides to bring X to one side alone:<BR>\n" );
document.write( "24 = 4X + 56  Subtract 56 from both sides:<BR>\n" );
document.write( "-32 = 4X  Divide by 4 on both sides:<BR>\n" );
document.write( "X = -8\r<BR>\n" );
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document.write( "Going back to the problem, we're supposed to find 4 consecutive even integers so the first is -8, the next would be -6, -4, -2.\r<BR>\n" );
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document.write( "Let's check:<BR>\n" );
document.write( "4 times the sum of the 1st and 4th:<BR>\n" );
document.write( "sum of the 1st and 4th is -8 + -2 = -10<BR>\n" );
document.write( "4 times that is -40<BR>\n" );
document.write( "8 greater than 12 times the third: <BR>\n" );
document.write( "12 times the 3rd is 12 x -4 = -48<BR>\n" );
document.write( "adding the 8 we get -48 + 8 = -40<BR>\n" );
document.write( "-40 = -40  Correct!\r<BR>\n" );
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document.write( "Answer:  -8, -6, -4, -2\r<BR>\n" );
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document.write( "Hope this helps so you can do more problems like this with more confidence.  Good luck!! </SPAN>\n" );
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