If \begin{vmatrix} 2x & 5 \ 8 & x \end{vmatrix} = \begin{vmatrix} 6 & 2 \ 7 & 3 \end{vmatrix}, write the value of x.

Compute the determinants as shown below:
\begin{vmatrix} 2x & 5 \ 8 & x \end{vmatrix} = \begin{vmatrix} 6 & 2 \ 7 & 3 \end{vmatrix}
(2x)(x) - (8)(5) = 6 \times 3 - 2 \times 7
\Rightarrow 2x^2 - 40 = 18 - 14
\Rightarrow 2x^2 - 40 = 4
\Rightarrow 2x^2 = 44
\Rightarrow x^2 = 22
\Rightarrow x = \pm \sqrt{22}