If \(\begin{vmatrix} 2 & 3 \\ 5 & 3x \end{vmatrix}\) = \(\begin{vmatrix} 4 & 1 \\ 3 & 2x \end{vmatrix}\), find the value of x.
A
-6
B
6
C
-12
D
12
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
\(\begin{vmatrix} 2 & 3 \\ 5 & 3x \end{vmatrix}\) = \(\begin{vmatrix} 4 & 1 \\ 3 & 2x \end{vmatrix}\)
(2 x 3x) - (5 x 3) = (4 x 2x) - (3 x 1)
6x - 15 = 8x - 3
6x - 8x = 15 - 3
-2x = 12
x = \(\frac{12}{-2}\)
= -6
Source: Myschool Past Questions Archive (Record #29429)