Question

If the five expressions 2x + 1, 2x - 3, x + 2, x + 5 and x - 3 can be arranged in a different order so that the first three have a sum of 4x + 4 and the last three have a sum of 4x + 3 what will the expression in the middle be?

Answer 1

To find the expression in the middle, we first need to combine the given expressions into two groups - one with a sum of 4x + 4 and the other with a sum of 4x + 3.

From the expressions given:
2x + 1 + 2x - 3 + x + 2 = 5x
x + 2 + x + 5 + x - 3 = 3x + 4

Therefore, the two groups are:
5x and 3x + 4

To arrange them in the desired order:
5x, (middle expression), 3x + 4

Now, to find the middle expression:
5x + (middle expression) + 3x + 4 = 4x + 4
8x + (middle expression) + 4 = 4x + 4
8x + (middle expression) = 4x
(middle expression) = 4x - 8x
(middle expression) = -4x

Therefore, the expression in the middle is -4x.