Question

If $\left|\begin{array}{cc}2x& x+3\\ 2\left(x+1\right)& x+1\end{array}\right|=\left|\begin{array}{cc}1& 5\\ 3& 3\end{array}\right|$, then write the value of x.

Answer 1

$$\begin{gathered} \left|\begin{array}{cc}2x& x+3\\ 2\left(x+1\right)& x+1\end{array}\right|=\left|\begin{array}{cc}1& 5\\ 3& 3\end{array}\right| \\ \Rightarrow \left(2x\right)\left(x+1\right)-2\left(x+1\right)\left(x+3\right)=3-15 \\ \Rightarrow \left(x+1\right)\left(2x-2x-6\right)=-12 \\ \Rightarrow -6x-6=-12 \\ \Rightarrow -6x=-6 \\ \Rightarrow x=1 \\ \mathrm{Hence},\mathrm{the}\mathrm{value}\mathrm{of}x\mathrm{is}1. \end{gathered}$$