$\frac{1}{2} - \frac{1}{3} = \frac{3}{x}$. What is the value of $x$?

$$\boxed{ \small{\text{ ~~$\frac{1}{2} - \frac{1}{3} = \frac{3}{x}$. What is the value of $x$~? }}}\\\\\\ \small{\text{$ \begin{array}{rcl} \dfrac{1}{2} - \dfrac{1}{3} &=& \dfrac{3}{x}\\\\ \dfrac{1}{2}\cdot\dfrac33 - \dfrac{1}{3}\cdot\dfrac22 &=& \dfrac{3}{x}\\\\ \dfrac{3-2}{6} &=& \dfrac{3}{x}\\\\ \dfrac{1}{6} &=& \dfrac{3}{x}\\\\ \dfrac{6}{1} &=& \dfrac{x}{3}\\\\ 6 &=& \dfrac{x}{3}\\\\ \dfrac{x}{3} &=& 6 \quad | \quad \cdot 3\\\\ x &=& 6 \cdot 3\\\\ \mathbf{x} & \mathbf{=} & \mathbf{18}\\\\ \end{array} $}}$$