Question

Determinati x apartine Z, a) -3/2x-1 apartine Z:,b) 6/-x+3 apartine Z.

Answer 1

$a) \frac{ - 3}{2x - 1} \: \in \: \mathbb{Z} = > 2x - 1 \: \in \: D_{-3}$

$D_{-3}=\left \{ \pm1,\pm3 \right \}$

$1)2x - 1 = - 1$

$2x = - 1 + 1$

$2x = 0\:|\div2$

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

$2)2x - 1 = 1$

$2x = 1 + 1$

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

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

$3)2x - 1 = - 3$

$2x = - 3 + 1$

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

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

$4)2x - 1 = 3$

$2x = 3 + 1$

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

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

$b) \frac{6}{ - x + 3} \: \in \: \mathbb{Z} = > - x + 3 \: \in\:D_{6}$

$D_{6} = \left \{ \pm1,\pm2,\pm3 ,\pm6\right \}$

$1) - x + 3 = - 1$

$- x = - 1 - 3$

$- x = - 4 \: | \times ( - 1)$

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

$2) - x + 3 = 1$

$- x = 1 - 3$

$- x = - 2 \: | \times ( - 1)$

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

$3) - x + 3 = - 2$

$- x = - 2 - 3$

$- x = - 5 \: | \times ( - 1)$

$x = 5 \: \in \: \mathbb{Z}$

$4) - x + 3 = 2$

$- x = 2 - 3$

$- x = - 1 \: | \times ( - 1)$

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

$5) - x + 3 = - 3$

$- x = - 3 - 3$

$- x = - 6 \: | \times ( - 1)$

$x = 6 \: \in \: \mathbb{Z}$

$6) - x + 3 = 3$

$- x = 3 - 3$

$- x = 0 \: | \times ( - 1)$

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

$7) - x + 3 = - 6$

$- x = - 6 - 3$

$- x = - 9 \: | \times ( - 1)$

$x = 9 \: \in \: \mathbb{Z}$

$8) - x + 3 = 6$

$- x = 6 - 3$

$- x = 3 \: | \times ( - 1)$

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