If \( \begin{vmatrix} 4x & 9\\ -4 & -5\end{vmatrix}=\begin{vmatrix} 4 & 8\\ 2 & 3\end{vmatrix} \), then the value of \( x \) is :
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 2
Since \( \begin{vmatrix} a & b\\ c & d\end{vmatrix}=ad-bc \), expanding both determinants gives
\( \displaystyle 4x(-5)-9(-4)=4(3)-8(2) \)
\( \displaystyle -20x+36=-4 \)
\( \displaystyle -20x=-40 \)
\( \displaystyle x=2 \)