Question

Daca ( 2x+3) | 6 și x aparține Z , atunci x aparține .....

Answer 1

(2x+3) I 6
2x+3∈D6
2x+3∈{-6;-3;-2;-1;1;2;3;6}
2x∈{-9;-6;-5;-4;-2;-1;0;3}
x∈{-3;-2;-1;0;1}

Answer 2

$(2x+3) | 6 \Rightarrow (2x+3) \in D_6 \Rightarrow (2x+3) \in\Big\{\pm1; \pm2; \pm3; \pm6\Big\} \Rightarrow \\ \\ \Rightarrow (2x+3) \in \Big\{-6; -3; -2; -1; 1; 2; 3; 6\Big\} \Big|-3 \Rightarrow \\ \\ \Rightarrow 2x \in \Big\{-9; -6; -5; -4; -2; -1; 0; 3\Big\}\Big|:2 \Rightarrow \\ \\ \Rightarrow x \in\Big\{\dfrac{-9}{2};-3;\dfrac{-5}{2};-2;-1;\dfrac{-1}{2};0;\dfrac{3}{2}\Big\}, dar x\in \mathbb_{Z} \Rightarrow$

$\Rightarrow \boxed{x \in\Big\{-3; -2; -1; 0\Big\}}$