Answer
$x=\dfrac{13}{11}$
Work Step by Step
The determinant for a 3 by 3 matrix can be computed as:
$Determinant (D)= \begin{vmatrix} A & B & C \\
a & b & c \\
g &h & i \\ \end{vmatrix}=A(ei-fh)-B(di-fg)+C(dh-eg)$
We have:
$D= \begin{vmatrix}
x & 1 & 1 \\
4 & 3 & 2 \\
-1 & 2 & 5 \\ \end{vmatrix}
$
Therefore, $D=x (15-4)-(1)(20+2)+(1)(8+3) \\=11x-22+11 \\=11x-11$
Since, $det=2$
So, $11x-11=2 \implies 11x=13$
or, $x=\dfrac{13}{11}$