[tex]a) \frac{5}{x - 1} \: \in\: \mathbb{Z} = > (x - 1) \: \in \: D_{5}[/tex]
[tex]D_{5}=\left\{\pm1,\pm5\right\}[/tex]
[tex]1)x - 1 = - 1[/tex]
[tex]x = - 1 + 1[/tex]
[tex]x = 0 \: \in \: \mathbb{Z}[/tex]
[tex]2)x - 1 = 1[/tex]
[tex]x = 1 + 1[/tex]
[tex]x = 2 \: \in \: \mathbb{Z}[/tex]
[tex]3)x - 1 = - 5[/tex]
[tex]x = - 5 + 1[/tex]
[tex]x = - 4 \: \in \: \mathbb{Z}[/tex]
[tex]4)x - 1 = 5[/tex]
[tex]x = 5 + 1[/tex]
[tex]x = 6 \: \in \: \mathbb{Z}[/tex]
[tex] = > x \: \in \: \left\{-4,0,2,6\right\}[/tex]
[tex]b) |x - 5| = 1[/tex]
[tex]1)x - 5 = 1[/tex]
[tex]x = 1 + 5[/tex]
[tex]x = 6[/tex]
[tex]2)x - 5 = - 1[/tex]
[tex]x = - 1 + 5[/tex]
[tex]x = 4[/tex]
[tex]S=\left\{4,6\right\}[/tex]
