Solve:

$x + 7 -\dfrac{8x}{3} = \dfrac{17x}{6} - \dfrac{5x}{8}$

$x + 7 -\dfrac{8x}{3} = \dfrac{17x}{6} - \dfrac{5x}{8}$

Since L.C.M. of denominators 6 and 8 = 24, multiply each term with 24 to get:

$⇒ x\times 24 + 7\times 24 -\dfrac{8x\times 24}{3} = \dfrac{17x \times 24}{6} - \dfrac{5x \times 24}{8}$

⇒ 24x + 168 - 8x $\times$ 8 = 17x $\times$ 4 - 5x $\times$ 3

⇒ 24x + 168 - 64x = 68x - 15x

⇒ 168 - 40x = 53x

⇒ - 53x - 40x = - 168

⇒ - 93x = - 168

⇒ x = $\dfrac{168}{93}$

⇒ x = $\dfrac{56}{31}$

⇒ x = $1\dfrac{25}{31}$

Hence, the value of x is $1\dfrac{25}{31}$