document.write( "Question 1091968: If the five expressions 2x + 1, 2x – 3, x + 2, x + 5, and x-3 are arranged correctly, the first three expressions have a sum of 4x +3, and the last three expressions have a sum of 4x + 4, what would the middle expression be? (For example, would 2x + 1 need to be the expression in the middle to make both sums possible?)
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Algebra.Com's Answer #706469 by Fombitz(32388)\"\" \"About 
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Since the first three terms and the last three terms sum to 4x.
\n" ); document.write( "The first term and the last terms must contain the 2x term and the middle terms contain the x term.
\n" ); document.write( "So then for the constant term, there are 12 possible combinations.
\n" ); document.write( "Six combinations of the middle 3 terms and two combinations of the outer terms.
\n" ); document.write( "Here's one,
\n" ); document.write( "(2,1)
\n" ); document.write( "(1,2)
\n" ); document.write( "(1,5)
\n" ); document.write( "(1,-3)
\n" ); document.write( "(2,-3)
\n" ); document.write( "So then the top three sums would be
\n" ); document.write( "(2+1+1,1+2+5)
\n" ); document.write( "(4,8)
\n" ); document.write( "4x+8
\n" ); document.write( "The bottom three sums would be,
\n" ); document.write( "(1+1+2,5-3-3)
\n" ); document.write( "(4,-1)
\n" ); document.write( "4x-1
\n" ); document.write( "You can apply some logic rules since each sum shares one term (the middle one) and narrow it down.
\n" ); document.write( "Work it our and see which combination works.
\n" ); document.write( "I used EXCEL to simplify but paper and pencil works just as well.
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