Solve :

$5x - (4x + \dfrac{5x - 4}{7}) = \dfrac{4x - 14}{3}$

$5x - (4x + \dfrac{5x - 4}{7}) = \dfrac{4x - 14}{3}\\[1em] ⇒ 5x - 4x - \dfrac{5x - 4}{7} = \dfrac{4x - 14}{3}\\[1em] ⇒ x - \dfrac{5x - 4}{7} = \dfrac{4x - 14}{3}\\[1em] ⇒ \dfrac{x}{1} - \dfrac{5x - 4}{7} = \dfrac{4x - 14}{3}\\[1em]$

Since L.C.M. of denominators 3 and 7 = 21, multiply each term with 21 to get:

$⇒ x \times 21 - \dfrac{(5x - 4)\times 21}{7} = \dfrac{(4x - 14) \times 21}{3}$

⇒ 21x - (5x - 4) $\times$ 3 = (4x - 14) \times 7

⇒ 21x - (15x - 12) = (28x - 98)

⇒ 21x - 15x + 12 = 28x - 98

⇒ 6x + 12 = 28x - 98

⇒ 6x - 28x = - 98 - 12

⇒ - 22x = - 110

⇒ x = $\dfrac{110}{22}$

⇒ x = 5

Hence, the value of x is 5.