Question

Solutiile intregi pozitive ale inecuatiei x-4(x-2)>-1

Answer 1

$\it x-4(x-2)>-1 \Rightarrow x-4x+8>-1 \Rightarrow x-4x>-1-8 \Rightarrow \\ \\ \\ \Rightarrow -3x>-9|_{\cdot(-1)} \Rightarrow 3x<9|_{:3} \Rightarrow x<3\ \ \ \ \ \ (1)\\ \\ \\ Dar,\ \ x\in\mathbb{Z}_{+}\ \ \ \ \ \ (2)\\ \\ \\ (1),\ (2) \Rightarrow x\in\{1,\ 2\}$