Answer
$\displaystyle \frac{13}{11}$
Work Step by Step
2 by 2 determinant: $D=\left|\begin{array}{ll}
a & b\\
c & d
\end{array}\right|=ad-bc$
3 by 3 determinant:
$\left|\begin{array}{lll}
{a_{11}}&{a_{12}}&{a_{13}}\\
{a_{21}}&{a_{22}}&{a_{23}}\\
{a_{31}}&{a_{32}}&{a_{33}}\end{array}\right|=\\\\=a_{11}\left|\begin{array}{cc}
{a_{22}}&{a_{23}}\\
{a_{32}}&{a_{33}}\end{array}\right|-a_{12}\left|\begin{array}{cc}
{a_{21}}&{a_{23}}\\
{a_{31}}&{a_{33}}\end{array}\right|+a_{13}\left|\begin{array}{cc}
{a_{21}}&{a_{22}}\\{a_{31}}&{a_{32}}\end{array}\right|$
---
$\left|\begin{array}{rrr}{x}&{1}&{1}\\{4}&{3}&{2}\\{-1}&{2}&{5}\end{array}\right|=x\left|\begin{array}{cc}
{3}&{2}\\{2}&{5}\end{array}\right|-1\left|\begin{array}{cc}{4}&{2}\\{-1}&{5}\end{array}\right|+1\left|\begin{array}{cc}{4}&{3}\\{-1}&{2}\end{array}\right|$
$=x(15-4)-(20+2)+(8+3)$
$=11x-22+11$
$= 11x -11$
So, we are solving
$11x -11=2$
$11x=13$
$x=\displaystyle \frac{13}{11}$
