Question:
If $\left|\begin{array}{cc}3 x & 7 \\ -2 & 4\end{array}\right|=\left|\begin{array}{ll}8 & 7 \\ 6 & 4\end{array}\right|$, find the value of $x .$
Solution:
$\left|\begin{array}{ll}3 x & 7 \\ -2 & 4\end{array}\right|=\left|\begin{array}{ll}8 & 7 \\ 6 & 4\end{array}\right|$
$\Rightarrow 12 x+14=32-42$
$\Rightarrow 12 x+14=-10$
$\Rightarrow 12 x=-24$
$\Rightarrow x=-2$
$\therefore x=-2 .$
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