It is given that (5x + 2),(4x - 1) and (x + 2) are in AP.
∴ (4x - 1) - (5x + 2) = (x + 2) - (4x - 1)
\(\Rightarrow\) 4x - 1 - 5x - 2 = x + 2 - 4x + 1
\(\Rightarrow\) -x - 3 = -3x + 3
\(\Rightarrow\) 3x - x = 3 + 3
\(\Rightarrow\) 2x = 6
\(\Rightarrow\) x = 3
Hence, the value of x is 3.
