Solve (question no. 2-22) for x :

$\dfrac{2x - 13}{5} - \dfrac{x - 3}{11} = \dfrac{x - 9}{5} + 1$

$\dfrac{2x - 13}{5} - \dfrac{x - 3}{11} = \dfrac{x - 9}{5} + 1$

Since L.C.M. of denominators 5 and 11 = 55, multiply each term by 55 to get:

$⇒ \dfrac{(2x - 13) \times 55}{5} - \dfrac{(x - 3) \times 55}{11} = \dfrac{(x - 9) \times 55}{5} + 1 \times 55\\[1em]$

⇒ 11 (2x - 13) - 5 (x - 3) = 11 (x - 9) + 55

⇒ (22x - 143) - (5x - 15) = (11x - 99) + 55

⇒ 22x - 143 - 5x + 15 = 11x - 99 + 55

⇒ 17x - 128 = 11x - 44

⇒ 17x - 11x = 128 - 44

⇒ 6x = 84

⇒ x = $\dfrac{84}{6}$

⇒ x = 14

Hence, the value of x is 14.