Answer
$x=4$
Work Step by Step
$\left|\begin{array}{lll}
a_{1} & b_{1} & c_{1}\\
a_{2} & b_{2} & c_{2}\\
a_{3} & b_{3} & c_{3}
\end{array}\right| =$
$=a_{1}b_{2}c_{3}+b_{1}c_{2}a_{3}+c_{1}a_{2}b_{3}-a_{3}b_{2}c_{1}-b_{3}c_{2}a_{1}-c_{3}a_{2}b_{1}$
---------------------
$\left|\begin{array}{lll}
1 & x & -2\\
3 & 1 & 1\\
0 & -2 & 2
\end{array}\right|$
$=1(1)(2)+x(1)(0)+(-2)(3)(-2)-0(1)(-2) - (-2)(1)(1)-2(3)(x)$
$=2+12+2-6x=16-6x$
$16-6x=-8\qquad/-16$
$-6x=-24\qquad/\div(-6)$
$x=4$
