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

$\dfrac{a + 5}{6} - \dfrac{a + 1}{9} = \dfrac{a + 3}{4}$

$\dfrac{a + 5}{6} - \dfrac{a + 1}{9} = \dfrac{a + 3}{4}$

Since L.C.M. of denominators 6, 9 and 4 = 36, multiply each term by 36 to get:

$⇒ \dfrac{36(a + 5)}{6} - \dfrac{36(a + 1)}{9} = \dfrac{36(a + 3)}{4}$

⇒ 6(a + 5) - 4(a + 1) = 9(a +3)

⇒ (6a + 30) - (4a + 4) = (9a + 27)

⇒ 6a + 30 - 4a - 4 = 9a + 27

⇒ 2a + 26 = 9a + 27

⇒ 2a - 9a = 27 - 26

⇒ - 7a = 1

⇒ a = -$\dfrac{1}{7}$

Hence, the value of a is $-\dfrac{1}{7}$.