a: \(\Leftrightarrow-\dfrac{23}{5}\cdot\dfrac{50}{23}< =x< =\dfrac{-13}{5}:\dfrac{21}{15}\)

=>-10<=x<=-13/7

hay \(x\in\left\{-10;-9;...;-2\right\}\)

b: \(\Leftrightarrow-\dfrac{13}{3}\cdot\dfrac{1}{3}< =x< =-\dfrac{2}{3}\cdot\dfrac{-11}{12}\)

=>-13/9<=x<=11/18

hay \(x\in\left\{-1;0\right\}\)

\(\Leftrightarrow-\dfrac{13}{3}\cdot\dfrac{1}{3}< =x< =\dfrac{-2}{3}\cdot\dfrac{4-6-9}{12}\)

\(\Leftrightarrow-\dfrac{13}{9}< =x< =\dfrac{-2}{3}\cdot\dfrac{-11}{12}=\dfrac{22}{36}=\dfrac{11}{18}\)

mà x là số nguyên

nên \(x\in\left\{-1;0;1\right\}\)

a. \(\dfrac{1}{2}-\left(\dfrac{1}{3}+\dfrac{3}{4}\right)\le x\le\dfrac{1}{24}.\left(\dfrac{1}{3}-\dfrac{1}{3}\right)\)

\(\dfrac{1}{2}-\dfrac{13}{12}\le x\le\dfrac{1}{24}.0\) ( lười viết nên điền kết quả luôn )

\(\dfrac{-7}{12}\le x\le0\)

\(0,5833...\le x\le0\)

Vì \(x\in Z\)\(\Rightarrow x\in\left\{0\right\}\)

Vậy...

b. \(-4\dfrac{1}{3}\left(\dfrac{1}{2}+\dfrac{1}{6}\right)\le x\le\dfrac{-2}{3}\left(\dfrac{1}{3}-\dfrac{1}{2}.\dfrac{3}{4}\right)\)

\(\dfrac{-26}{9}\le x\le\dfrac{1}{36}\)

\(-2,8888...\le x\le0,277...\)

Vì \(x\in Z\Rightarrow x\in\left\{-2;-1;0\right\}\)

Vậy ...

\(-1\dfrac{4}{9}\le x\le-\dfrac{11}{18}\)

Vì x là số nguyên nên x = -1

7) \(\dfrac{-5}{17}+\dfrac{3}{17}\le\dfrac{x}{17}\le\dfrac{13}{17}+\dfrac{-11}{17}\)

\(\Rightarrow\dfrac{-2}{17}\le\dfrac{x}{17}\le\dfrac{2}{17}\)

\(\Rightarrow-2\le x\le2\)

\(\Rightarrow x\in\left\{-2;-1;0;1;2\right\}\)

8) \(\dfrac{2}{3}\left(\dfrac{1}{2}+\dfrac{3}{4}-\dfrac{1}{3}\right)\le\dfrac{x}{18}\le\dfrac{7}{3}\left(\dfrac{1}{2}-\dfrac{1}{6}\right)\)

\(\Rightarrow\dfrac{2}{3}\left(\dfrac{6}{12}+\dfrac{9}{12}-\dfrac{4}{12}\right)\le\dfrac{x}{18}\le\dfrac{7}{3}\left(\dfrac{6}{12}-\dfrac{2}{12}\right)\)

\(\Rightarrow\dfrac{2}{3}\cdot\dfrac{11}{12}\le\dfrac{x}{18}\le\dfrac{7}{3}\cdot\dfrac{4}{12}\)

\(\Rightarrow\dfrac{22}{36}\le\dfrac{x}{18}\le\dfrac{28}{36}\)

\(\Rightarrow\dfrac{11}{18}\le\dfrac{x}{18}\le\dfrac{14}{18}\)

\(\Rightarrow x\in\left\{11;12;13;14\right\}\)

8) \(\dfrac{2}{3}\left(\dfrac{1}{2}+\dfrac{3}{4}-\dfrac{1}{3}\right)\le\dfrac{x}{18}\le\dfrac{7}{3}\left(\dfrac{1}{2}-\dfrac{1}{6}\right)\\ \dfrac{2}{3}\left(\dfrac{6}{12}+\dfrac{9}{12}-\dfrac{4}{12}\right)\le\dfrac{x}{18}\le\dfrac{7}{3}\left(\dfrac{3}{6}-\dfrac{1}{6}\right)\\ \dfrac{2}{3}.\dfrac{11}{12}\le\dfrac{x}{18}\le\dfrac{7}{3}.\dfrac{2}{6}\\ \dfrac{11}{18}\le\dfrac{x}{18}\le\dfrac{14}{18}\\ \Rightarrow11\le x\le14\\ \Rightarrow x\in\left\{11;12;13;14\right\}\)

7) \(\dfrac{-5}{17}+\dfrac{3}{17}\le\dfrac{x}{17}\le\dfrac{13}{17}+\dfrac{-11}{17}\\ \dfrac{-2}{17}\le\dfrac{x}{17}\le\dfrac{2}{17}\\ \Rightarrow-2\le x\le2\\ \Rightarrow x\in\left\{-2;-1;0;1;2\right\}\)

Câu 1: D

Câu 3: 53/144>9/170>9/230

a) \(\left(\dfrac{1}{12}+3\dfrac{1}{6}-30.75\right).x-8=\left(\dfrac{3}{5}+0.415\right)\)

\(=\left(\dfrac{1}{12}+3\dfrac{1}{6}-\dfrac{123}{4}\right).x-8=\left(\dfrac{3}{5}+\dfrac{83}{200}\right)\)

\(=\dfrac{-55}{2}.x-8=\dfrac{203}{200}\)\(=\dfrac{-55}{2}.x=\dfrac{203}{200}+8=\dfrac{1803}{200}\)

\(x=\dfrac{1803}{200}:\dfrac{-55}{2}=\dfrac{-1803}{5500}\)

a, \(\left(\dfrac{1}{12}+3\dfrac{1}{6}-30,75\right).x-8=\dfrac{3}{5}+0,415\)

\(\left(\dfrac{1}{12}+3\dfrac{1}{6}-30,75\right).x-8=\dfrac{203}{200}\)

\(\left(\dfrac{1}{12}+3\dfrac{1}{6}-30,75\right).x=\dfrac{203}{200}+8\)

\(\left(\dfrac{1}{12}+3\dfrac{1}{6}-30,75\right).x=\dfrac{1803}{200}\)

\(\left(\dfrac{13}{4}-30,75\right).x=\dfrac{1803}{200}\)

\(\dfrac{-55}{2}.x=\dfrac{1803}{200}\)

\(x=\dfrac{1803}{200}:\dfrac{-55}{2}\)

\(x=\dfrac{-1803}{5500}\)

Nếu là tìm số nguyên thì hình như đề sai rồi bạn
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b, \(4\dfrac{1}{3}.\left(\dfrac{1}{6}-\dfrac{1}{2}\right)\le x\le\dfrac{2}{3}.\left(\dfrac{1}{3}-\dfrac{1}{2}-\dfrac{3}{4}\right)\)

Cho \(A=4\dfrac{1}{3}.\left(\dfrac{1}{6}-\dfrac{1}{2}\right)\)

\(A=4\dfrac{1}{3}.\dfrac{-1}{3}\)

\(A=\dfrac{13}{3}.\dfrac{-1}{3}\)

\(A=\dfrac{-13}{9}\)

Cho \(B=\dfrac{2}{3}.\left(\dfrac{1}{3}-\dfrac{1}{2}-\dfrac{3}{4}\right)\)

\(B=\dfrac{2}{3}.\left(\dfrac{-1}{6}-\dfrac{3}{4}\right)\)

\(B=\dfrac{2}{3}.\dfrac{-11}{12}\)

\(B=\dfrac{-11}{18}\)

Ta có: \(A\le x\le B\)

\(\dfrac{-13}{9}\le x\le\dfrac{-11}{18}\)

\(\Rightarrow x=-1\)

\(\Leftrightarrow\dfrac{3}{7}\left(\dfrac{46}{3}+\dfrac{12}{5}\right)< =x< =\left(\dfrac{10}{3}:7-\dfrac{13}{2}\right)\cdot\dfrac{-7}{3}\)

\(\Leftrightarrow\dfrac{38}{5}< =x< =\dfrac{253}{18}\)

mà x là số nguyên

nên \(x\in\left\{8;9;10;11;12;13;14\right\}\)