Question

Aflați x € Z asa incat 9 pe x+4 € Z

Answer 1

9/(x+4)  ∈Z,    x≠-4
=> x+4| 9; x+4={-9,-3,-1,1,3,9}  (scadem 4 si obtinem x)
              deci x={-13,-7,-5,-3,-1,5}

Answer 2

[tex]\it \dfrac{9}{x+4} \in \mathbb{Z} \Rightarrow x+4|9 \Rightarrow x+4 \in D_9 \Rightarrow x+4 \in \{\pm1,\ \pm3,\ \pm9\} \Rightarrow \\\;\\ \\\;\\ \Rightarrow x + 4 \in \{-9,\ -3,\ -1,\ 1,\ 3, \ 9\}|_{-4} \Rightarrow \\\;\\ \\\;\\ \Rightarrow x\in\{-13,\ -7,\ -5,\ -3\ -1,\ 5\}[/tex]