Solve:

$\dfrac{9x + 7}{2} - (x - \dfrac{x - 2}{7}) = 36$

$\dfrac{9x + 7}{2} - (x - \dfrac{x - 2}{7}) = 36\\[1em] ⇒ \dfrac{9x + 7}{2} - x + \dfrac{x - 2}{7} = 36\\[1em] ⇒ \dfrac{9x + 7}{2} - \dfrac{x}{1} + \dfrac{x - 2}{7} = 36$

Since L.C.M. of denominators 2 and 7 = 14, multiply each term with 14 to get:

$⇒ \dfrac{14(9x + 7)}{2} - \dfrac{x \times 14}{1} + \dfrac{14(x - 2)}{7} = 36 \times 14$

⇒ 7(9x + 7) - x $\times$ 14 + 2(x - 2) = 504

⇒ (63x + 49) - 14x + (2x - 4) = 504

⇒ 63x + 49 - 14x + 2x - 4 = 504

⇒ 51x + 45 = 504

⇒ 51x = 504 - 45

⇒ 51x = 459

⇒ x = $\dfrac{459}{51}$

⇒ x = 9

Hence, the value of x is 9.