If $\begin{vmatrix} 2x & 5 \\ 8 & x \end{vmatrix} = \begin{vmatrix} 6 & -2 \\ 7 & 3 \end{vmatrix}$, then the value of $x$ is

$\pm 6$

The correct answer is Option (3) → $\pm 6$ ##

We have, $\begin{vmatrix} 2x & 5 \\ 8 & x \end{vmatrix} = \begin{vmatrix} 6 & -2 \\ 7 & 3 \end{vmatrix}$

$\Rightarrow 2x^2 - 40 = 18 + 14$

$\Rightarrow 2x^2 = 32 + 40$

$\Rightarrow x^2 = \frac{72}{2} = 36$

$∴x = \pm 6$