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For matrix $$ \begin{bmatrix}5 - x & x + 1 \\2 & 4\end{bmatrix} $$ being singular $$ \Bigg|\begin{matrix} 5 - x & x + 1 \\2 & 4\end{matrix}\Bigg| = 0$$ $$\Rightarrow 20 - 4x - 2x - 2 = 0 $$ $$\Rightarrow 18 - 6x = 0 $$ $$\Rightarrow 6x = 18$$ $$\Rightarrow x = \cfrac{18}{6} = 3 $$
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