Question

Tìm x thuộc Z,biết:

\(\dfrac{-2}{7}\)<\(\dfrac{x}{3}\)<\(\dfrac{11}{4}\)

Answer 1

\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{x}{3}>\dfrac{-2}{7}\\\dfrac{x}{3}< \dfrac{11}{4}\end{matrix}\right.\) \(\begin{matrix}\left(1\right)\\\left(2\right)\end{matrix}\)

(1) <=> \(\dfrac{x}{3}+\dfrac{2}{7}>0\Leftrightarrow\dfrac{7x+6}{21}>0\Leftrightarrow7x+6>0;x>-\dfrac{6}{7}\) \(x\in z\Rightarrow x\ge0\)(a)

(2)<=>\(\dfrac{x}{3}-\dfrac{11}{4}< 0;4x-33< 0;x< \dfrac{33}{4};x\in z;x\le8\) (b)

từ (a) và (b) => x ={0;1;2;3;4;5'6;7;8}