Answer
$x=-\frac{4}{3}$
Work Step by Step
We find the determinant of the given matrix as follows:
$\begin{vmatrix} 5 & x \\ -3 & 2 \\ \end{vmatrix} =(5)(2) -(-3)(x) =10+3x$
Substitute the expression of the determinant in the given equation:
$10+3x=6$
Solve for $x$:
$3x=-4 \Rightarrow x=-\frac{4}{3}$
The solution of the given equation is
$x=-\frac{4}{3}$
