Question

[Trần Thị Trúc Linh]

Tìm tập hợp các số nguyên \(x\), biết:

a) \(4\dfrac{5}{9}:2\dfrac{5}{8}-7< x< \left(3\dfrac{1}{5}:3,2+4,5.1\dfrac{31}{45}\right):\left(-21\dfrac{1}{2}\right)\)

b) \(\dfrac{-17}{21}:\left(\dfrac{5}{4}-\dfrac{2}{5}\right)< x+\dfrac{4}{7}< 1-\dfrac{1}{2}+\dfrac{1}{3}-\dfrac{1}{4}\)

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Answer 1

[DƯƠNG PHAN KHÁNH DƯƠNG]

a )

\(4\dfrac{5}{9}:2\dfrac{5}{8}-7=-\dfrac{995}{189}=-5\) ( đã làm tròn )

\(\left(3\dfrac{1}{5}:3,2+4,5.1\dfrac{31}{45}\right):\left(-21\dfrac{1}{2}\right)\) \(=\dfrac{2}{5}=0\) ( đã làm tròn )

Ta có :

\(-5< x< 0\)

\(\Rightarrow x=\left\{-4;-3;-2;-1\right\}\)

b )

\(-\dfrac{17}{21}:\left(\dfrac{5}{4}-\dfrac{2}{5}\right)=-\dfrac{20}{21}=-1\) ( đã làm tròn )

\(1-\dfrac{1}{2}+\dfrac{1}{3}-\dfrac{1}{4}=\dfrac{7}{12}=1\) ( đã làm tròn )

Ta có : \(-1< x+0,6< 1\)

\(\Rightarrow x=\left\{-1;0\right\}\)

Answer 2

[qwerty]

a) \(4\dfrac{5}{9}:2\dfrac{5}{8}-7< x< \left(3\dfrac{1}{5}:3,2+4,5\cdot1\dfrac{31}{45}\right):\left(-21\dfrac{1}{2}\right)\)

\(\Leftrightarrow\left\{{}\begin{matrix}x>4\dfrac{5}{9}:2\dfrac{5}{8}-7\\x< \left(3\dfrac{1}{5}:3,2+4,5\cdot1\dfrac{31}{45}\right):\left(-21\dfrac{1}{2}\right)\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x>-\dfrac{227}{36}\\x< -\dfrac{2}{5}\end{matrix}\right.\)

\(\Leftrightarrow-\dfrac{2}{5}>x>-\dfrac{227}{36}\)

b) \(-\dfrac{17}{21}:\left(\dfrac{5}{4}-\dfrac{2}{5}\right)< x+\dfrac{4}{7}< 1-\dfrac{1}{2}+\dfrac{1}{3}-\dfrac{1}{4}\)

\(\Leftrightarrow\left\{{}\begin{matrix}x+\dfrac{4}{7}>-\dfrac{17}{21}:\left(\dfrac{5}{4}-\dfrac{2}{5}\right)\\x+\dfrac{4}{7}< 1-\dfrac{1}{2}+\dfrac{1}{3}-\dfrac{1}{4}\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x>-\dfrac{32}{21}\\x< \dfrac{1}{84}\end{matrix}\right.\)

\(\Leftrightarrow\dfrac{1}{84}>x>-\dfrac{32}{21}\)