"Rezolvaţi în mathbb Z a) 2x - 3 <= 7 e) 8 < 9 - x"
[tex]\it Rezolva\c{\it t}i\ pentru\ x\in\mathbb{Z}:\\ \\ a)\ \ 2x-3\leq7;\\ \\ e)\ \ 8<9-x\\ \\ c)\ 4-2x\geq10[/tex]
Rezolvare:
[tex]\it 2x-3\leq7|_{+3} \Rightarrow 2x\leq10|_{:2} \Rightarrow x\leq5 \Rightarrow x\in\{...,\ -2,\ -1,\ 0,\ 1,\ 2,\ 3,\ 4,\ 5\}[/tex]
[tex]\it e)\ 8<9-x \Rightarrow 8-9<-x \Rightarrow -1<-x|_{\cdot(-1)} \Rightarrow 1>x \Rightarrow x<1 \Rightarrow \\ \\ \\ x\in\{...,\ -3,\ -2,\ -1,\ 0\}[/tex]