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

$\dfrac{x}{3} - 2\dfrac{1}{2} = \dfrac{4x}{9} - \dfrac{2x}{3}$

$\dfrac{x}{3} - 2\dfrac{1}{2} = \dfrac{4x}{9} - \dfrac{2x}{3}\\[1em] ⇒ \dfrac{x}{3} - \dfrac{5}{2} = \dfrac{4x}{9} - \dfrac{2x}{3}\\[1em]$

Since L.C.M. of denominators 3, 2 and 9 = 18, multiply each term by 18 to get:

⇒ $\dfrac{18 \times x}{3} - \dfrac{18 \times 5}{2} = \dfrac{18 \times 4x}{9} - \dfrac{18 \times 2x}{3}$

⇒ 6x - 9 $\times$ 5 = 2 $\times$ 4x - 6 $\times$ 2x

⇒ 6x - 45 = 8x - 12x

⇒ 6x + 4x = 45

⇒ 10x = 45

⇒ x = $\dfrac{45}{10}$

⇒ x = 4.5

Hence, the value of x is 4.5.