If $\left|\begin{array}{cc}3 & -4 \\ 2 & 1\end{array}\right|=\left|\begin{array}{cc}2 x & 5 \\ 1 & x\end{array}\right|$ then $|x|$ is equal to

$2 \sqrt{2}$

$\left|\begin{array}{cc}3 & -4 \\ 2 & 1\end{array}\right|=\left|\begin{array}{cc}2 x & 5 \\ 1 & x\end{array}\right|$

$\Rightarrow 3-(-4) \times 2=2 x^2-5$

$\Rightarrow 3+8=2 x^2-5$

so $2 x^2=16$

⇒ so $x^2=8$

$|x| = 2 \sqrt{2}$