For what value of x, the following matrix is singular?

If a matrix $A$ is singular, then $|A|=0$

$\therefore\left|\begin{array}{cc}5-x & x+1 \\ 2 & 4\end{array}\right|=0$

$\Rightarrow 4(5-x)-2(x+1) 0$

$\Rightarrow 20-4 x-2 x-2$

$\Rightarrow 18-6 x=0$

$\Rightarrow 18=6 x$

$\Rightarrow x=3$