Question

aflati numarul natural x ≥ 2 pentru care 3/15 - 4/(x-1) ≤ 4/3

Answer 1

$\left \dfrac{3}{15}- \dfrac{4}{x-1}\leq\dfrac{4}{3} \right|\cdot 15 \\ \\ 3-\dfrac{60}{x-1}\leq 20 \\ \\ 3-20\leq \dfrac{60}{x-1} \\ \\ \dfrac{60}{x-1}\geq -17\Big|\cdot (x-1)\\ \\ ( putem inmulti cu x - 1 deoarece pe noi ne intereseaza doar cand x \geq 2 \\ , iar cand x \geq , si x - 1 \geq 2) \\ \\ 60 \geq -17(x-1) \Big|:(-17) \\ \\ -\dfrac{60}{17} \leq x-1 \\ \\ 1-\dfrac{60}{17}\leq x \\ \\ \dfrac{17-60}{17}\leq x \\ \\ -\dfrac{43}{17}\leq x \\ \\ x \geq -\dfrac{43}{17}$

$\Rightarrow x\in \Big\{2,3,4,5,6,7,8,...,\infty\Big\}$