ANSWER:
The value of x is 2
STEP-BY-STEP EXPLANATION:
We have the following equation:
[tex]\det \begin{pmatrix}4 & -1 \\ -4 & x\end{pmatrix}=\det \: \begin{pmatrix}5 & 3x \\ 1 & 2\end{pmatrix}[/tex]We solve as follows:
[tex]\begin{gathered} \det \begin{pmatrix}4 & -1 \\ -4 & x\end{pmatrix}=4\cdot x-(-4)\cdot(-1)=4x-4 \\ \det \: \begin{pmatrix}5 & 3x \\ \: 1 & 2\end{pmatrix}=5\cdot2-1\cdot3x=10-3x \\ \text{therefore:} \\ 4x-4=10-3x \\ 4x+3x=10+4 \\ 7x=14 \\ x=\frac{14}{7} \\ x=2 \end{gathered}[/tex]