Question

Va rog Ajutați-mă. După 21 Supra 2x-1 este aparține

Answer 1

$A=\left \{ x\:\in\:\mathbb{Z}\:|\: \frac{21}{2x - 1} \:\in\:\mathbb{Z}\right \}$

$\frac{21}{2x - 1} \: \in \: \mathbb{Z} = > (2x - 1) \: \in \: D_{21}$

$D_{21}=\left \{ \pm1,\pm3,\pm7,\pm21 \right \}$

$1)2x - 1 = - 1$

$2x = - 1 + 1$

$2x = 0 \: | \div 2$

$x = 0 \: \in \: \mathbb{Z}$

$2)2x - 1 = 1$

$2x = 1 + 1$

$2x = 2 \: | \div 2$

$x = 1 \: \in \: \mathbb{Z}$

$3)2x - 1 = - 3$

$2x = - 3 + 1$

$2x = - 2 \: | \div 2$

$x = - 1 \: \in \: \mathbb{Z}$

$4)2x - 1 = 3$

$2x = 3 + 1$

$2x = 4 \: | \div 2$

$x = 2 \: \in \: \mathbb{Z}$

$5)2x - 1 = - 7$

$2x = - 7 + 1$

$2x = - 6 \: | \div 2$

$x = - 3 \: \in \: \mathbb{Z}$

$6)2x - 1 = 7$

$2x = 7 + 1$

$2x = 8 \: | \div 2$

$x = 4 \: \in \: \mathbb{Z}$

$7)2x - 1 = - 21$

$2x = - 21 + 1$

$2x = - 20 \: | \div 2$

$x = - 10 \: \in \: \mathbb{Z}$

$8)2x - 1 = 21$

$2x = 21 + 1$

$2x = 22 \: | \div 2$

$x = 11 \: \in \: \mathbb{Z}$

$x\:\in\:\left \{ -10,-3,-1,0,1 ,2,4,11\right \}$

$= > A=\left \{ -10,-3,-1,0,1 ,2,4,11\right \}$