SOLUTION: 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

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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?)
Found 2 solutions by Fombitz, MathTherapy:
Answer by Fombitz(32388)   (Show Source): You can put this solution on YOUR website!
Since the first three terms and the last three terms sum to 4x.
The first term and the last terms must contain the 2x term and the middle terms contain the x term.
So then for the constant term, there are 12 possible combinations.
Six combinations of the middle 3 terms and two combinations of the outer terms.
Here's one,
(2,1)
(1,2)
(1,5)
(1,-3)
(2,-3)
So then the top three sums would be
(2+1+1,1+2+5)
(4,8)
4x+8
The bottom three sums would be,
(1+1+2,5-3-3)
(4,-1)
4x-1
You can apply some logic rules since each sum shares one term (the middle one) and narrow it down.
Work it our and see which combination works.
I used EXCEL to simplify but paper and pencil works just as well.
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

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?)
Whatever the other person says makes ABSOLUTELY NO SENSE. Hence, I would not even waste my time reading through it. 

See the correct solution at: Problem # 1091971 

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