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Question
If \[\begin{vmatrix}2x & x + 3 \\ 2\left( x + 1 \right) & x + 1\end{vmatrix} = \begin{vmatrix}1 & 5 \\ 3 & 3\end{vmatrix}\], then write the value of x.
Solution
\[\begin{vmatrix}2x & x + 3 \\ 2\left( x + 1 \right) & x + 1\end{vmatrix} = \begin{vmatrix}1 & 5 \\ 3 & 3\end{vmatrix}\]
\[ \Rightarrow \left( 2x \right)\left( x + 1 \right) - 2\left( x + 1 \right)\left( x + 3 \right) = 3 - 15\]
\[ \Rightarrow \left( x + 1 \right)\left( 2x - 2x - 6 \right) = - 12\]
\[ \Rightarrow - 6x - 6 = - 12\]
\[ \Rightarrow - 6x = - 6\]
\[ \Rightarrow x = 1\]
Hence, the value of x is 1.
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