What is the value of x if 2x + 3 , x + 4 and 3x - 4 are terms of an AP?  

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As 2x + 3, x + 4 and 3x - 4 are terms of an AP, they have a common difference.

We can write this as:

(2x + 3) - (x + 4) = (x + 4) - ( 3x - 4)

=> 2x + 3 - x - 4 = x + 4 - 3x + 4

=> x - 1 = -2x + 8

=> 3x = 9

=> x = 9/3

=> x = 3

The required value is x = 3.

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