Question

Multimea valorilor intregi ale lui x pentru care
9/2x-3 € Z este...

Answer 1

$\dfrac{9}{2x-3}\in \mathbb_{Z} \Rightarrow (2x-3) \big| 9\Rightarrow (2x-3) \in D_{9} \Rightarrow \\ \\ \Rightarrow (2x-3)\in \Big\{\pm1,\pm3,\pm9\Big\} \Rightarrow (2x-3)\in \Big\{-9,-3,-1,1,3,9\Big\}\Big| +3 \Rightarrow \\ \\ \Rightarrow 2x\in\Big\{-6,0,2,4,6,12\Big\}\Big| :2 \Rightarrow \boxed{x \in \Big\{-3,0,1,2,3,6\Big\}}$