Question

If $\left|\begin{array}{cc}3x& 7\\ -2& 4\end{array}\right|=\left|\begin{array}{cc}8& 7\\ 6& 4\end{array}\right|$, find the value of x.

Answer 1

$$\begin{gathered} \left|\begin{array}{cc}3x& 7\\ -2& 4\end{array}\right|=\left|\begin{array}{cc}8& 7\\ 6& 4\end{array}\right| \\ \Rightarrow 12x+14=32-42 \\ \Rightarrow 12x+14=-10 \\ \Rightarrow 12x=-24 \\ \Rightarrow x=-2 \\ \therefore x=-2. \end{gathered}$$