[tex]A=\left \{ x\:\in\:\mathbb{Z}\:|\: \frac{21}{2x - 1} \:\in\:\mathbb{Z}\right \}[/tex]
[tex] \frac{21}{2x - 1} \: \in \: \mathbb{Z} = > (2x - 1) \: \in \: D_{21}[/tex]
[tex]D_{21}=\left \{ \pm1,\pm3,\pm7,\pm21 \right \}[/tex]
[tex]1)2x - 1 = - 1[/tex]
[tex]2x = - 1 + 1[/tex]
[tex]2x = 0 \: | \div 2[/tex]
[tex]x = 0 \: \in \: \mathbb{Z}[/tex]
[tex]2)2x - 1 = 1[/tex]
[tex]2x = 1 + 1[/tex]
[tex]2x = 2 \: | \div 2[/tex]
[tex]x = 1 \: \in \: \mathbb{Z}[/tex]
[tex]3)2x - 1 = - 3[/tex]
[tex]2x = - 3 + 1[/tex]
[tex]2x = - 2 \: | \div 2[/tex]
[tex]x = - 1 \: \in \: \mathbb{Z}[/tex]
[tex]4)2x - 1 = 3[/tex]
[tex]2x = 3 + 1[/tex]
[tex]2x = 4 \: | \div 2[/tex]
[tex]x = 2 \: \in \: \mathbb{Z}[/tex]
[tex]5)2x - 1 = - 7[/tex]
[tex]2x = - 7 + 1[/tex]
[tex]2x = - 6 \: | \div 2[/tex]
[tex]x = - 3 \: \in \: \mathbb{Z}[/tex]
[tex]6)2x - 1 = 7[/tex]
[tex]2x = 7 + 1[/tex]
[tex]2x = 8 \: | \div 2[/tex]
[tex]x = 4 \: \in \: \mathbb{Z}[/tex]
[tex]7)2x - 1 = - 21[/tex]
[tex]2x = - 21 + 1[/tex]
[tex]2x = - 20 \: | \div 2[/tex]
[tex]x = - 10 \: \in \: \mathbb{Z}[/tex]
[tex]8)2x - 1 = 21[/tex]
[tex]2x = 21 + 1[/tex]
[tex]2x = 22 \: | \div 2[/tex]
[tex]x = 11 \: \in \: \mathbb{Z}[/tex]
[tex]x\:\in\:\left \{ -10,-3,-1,0,1 ,2,4,11\right \}[/tex]
[tex] = > A=\left \{ -10,-3,-1,0,1 ,2,4,11\right \}[/tex]
