Question

Detrminati numarul natural x pentru care are loc inegalitatea x≤23pe3<x+1 Va rog sa ma ajutati
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Answer 1

$\text{x}\leq\dfrac{23}{3}\ \textless \ \text{x}+1\Big|-\text{x} \\ \\ 0\leq \dfrac{23}{3}-\text{x}\ \textless \ 1\Big|\cdot 3 \\ \\ 0\leq 23-3\text{x}\ \textless \ 3\Big|-23 \\ \\ -23\leq-3\text{x}\ \textless \ -20 \Big|\cdot (-1) \\ \\ 23\geq3\text{x}\ \textgreater \ 20 \\ \\ 20\ \textless \ 3\text{x}\leq 23 \Big|:3 \\ \\ \dfrac{20}{3}\ \textless \ \text{x}\leq\dfrac{23}{3} \\ \\ \text{x}\in \Big(\dfrac{20}{3};\dfrac{23}{3}\Big] \\ \\ \text{x} \in \Big(6,(6); 7,(6)\Big], dar, \text{x} \in \mathbb_{N} \Rightarrow \boxed{S= \Big\{7\Big\}}$