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.

 

 

Answer 1

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