If $\begin{vmatrix} 2 & 3 & 2 \\ x & x & x \\ 4 & 9 & 1 \end{vmatrix} + 3 = 0$, then the value of $x$ is:

$-1$

The correct answer is Option (3) → $-1$ ##

Given $\begin{vmatrix} 2 & 3 & 2 \\ x & x & x \\ 4 & 9 & 1 \end{vmatrix} + 3 = 0$

On expanding along $R_1$:

$2(x - 9x) - 3(x - 4x) + 2(9x - 4x) + 3 = 0$

$2(-8x) - 3(-3x) + 2(5x) + 3 = 0$

$-16x + 9x + 10x + 3 = 0$

$3x + 3 = 0$

$3x = -3$

$x = -\frac{3}{3}$

$x = -1$