If $a - 3 = \dfrac{a}{2} + \dfrac{a}{3}$, then the value of $a$ is

1. 12
2. 15
3. 18
4. 24

We have:

$\phantom{=} a - 3 = \dfrac{a}{2} + \dfrac{a}{3} \\[1em] \Rightarrow a - 3 = \dfrac{3a + 2a}{6} \\[1em] \Rightarrow 6(a - 3) = 5a \\[1em] \Rightarrow 6a - 18 = 5a \\[1em] \Rightarrow 6a - 5a = 18 \quad \text{[Transposing -18 to RHS and +5a to LHS]} \\[1em] \Rightarrow a = 18$

Hence, option 3 is the correct option.