[tex]B=\left \{ x\:\in\:\mathbb{Z} \:|\:\:\frac{6}{2x-1}\:\in\:\mathbb{Z}\right \}[/tex]
[tex] \frac{6}{2x - 1} \: \in \: \mathbb{Z} = > 2x - 1 \: \in \: D_{6}[/tex]
[tex]D_{6}=\left \{ \pm1,\pm2,\pm3,\pm6 \right \}[/tex]
[tex]1)2x - 1 = - 1[/tex]
[tex]2x = - 1 + 1[/tex]
[tex]2x = 0[/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 = - 2[/tex]
[tex]2x = - 2 + 1[/tex]
[tex]2x = - 1[/tex]
[tex]x = - \frac{1}{2} \: \notin \: \mathbb{Z}[/tex]
[tex]4)2x - 1 = 2[/tex]
[tex]2x = 2 + 1[/tex]
[tex]2x = 3[/tex]
[tex]x = \frac{3}{2} \: \notin \: \mathbb{Z}[/tex]
[tex]5)2x - 1 = - 3[/tex]
[tex]2x = - 3 + 1[/tex]
[tex]2x = - 2 \: | \div 2[/tex]
[tex]x = - 1 \: \in \: \mathbb{Z}[/tex]
[tex]6)2x - 1 = 3[/tex]
[tex]2x = 3 + 1[/tex]
[tex]2x = 4 \: | \div 2[/tex]
[tex]x = 2 \: \in \: \mathbb{Z}[/tex]
[tex]7)2x - 1 = - 6[/tex]
[tex]2x = - 6 + 1[/tex]
[tex]2x = - 5[/tex]
[tex]x = - \frac{5}{2} \: \notin \: \mathbb{Z}[/tex]
[tex]8)2x - 1 = 6[/tex]
[tex]2x = 6 + 1[/tex]
[tex]2x = 7[/tex]
[tex]x = \frac{7}{2} \: \notin \: \mathbb{Z}[/tex]
[tex] = > B=\left \{ -1,0,1,2\right \}[/tex]
[tex] = > cardB = 4[/tex]
