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Question
If \[\begin{vmatrix}3x & 7 \\ - 2 & 4\end{vmatrix} = \begin{vmatrix}8 & 7 \\ 6 & 4\end{vmatrix}\] , find the value of x.
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Solution
\[\begin{vmatrix}3x & 7 \\ - 2 & 4\end{vmatrix} = \begin{vmatrix}8 & 7 \\ 6 & 4\end{vmatrix}\]
\[ \Rightarrow 12x + 14 = 32 - 42\]
\[ \Rightarrow 12x + 14 = - 10\]
\[ \Rightarrow 12x = - 24\]
\[ \Rightarrow x = - 2\]
\[ \therefore x = - 2 .\]
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