Bài giải

a, \(3\frac{1}{3}\text{ : }2\frac{1}{2}-1< x< 7\frac{2}{3}\cdot\frac{3}{7}+\frac{5}{2}\)

\(\frac{10}{3}\text{ : }\frac{5}{2}-1< x< \frac{23}{3}\cdot\frac{3}{7}+\frac{5}{2}\)

\(\frac{4}{3}-1< x< \frac{23}{7}+\frac{5}{2}\)

\(\frac{1}{3}< x< \frac{81}{14}\)

\(\Rightarrow\text{ }0,\left(3\right)< x< 5,78...\)

\(\Rightarrow\text{ }x\in\left\{1\text{ ; }2\text{ ; }3\text{ ; }4\text{ ; }5\right\}\)

b, \(\frac{1}{2}-\left(\frac{1}{3}+\frac{1}{4}\right)< x< \frac{1}{48}-\left(\frac{1}{16}-\frac{1}{6}\right)\)

\(\frac{1}{2}-\frac{7}{12}< x< \frac{1}{48}+\frac{5}{48}\)

\(-\frac{1}{12}< x< \frac{1}{8}\)

\(\Rightarrow\text{ }-0,08\left(3\right)< x< 0,125\)

\(\Rightarrow\text{ }x\in\varnothing\)

1. \(\frac{-7}{12}\)< \(\frac{x-1}{4}\)< \(\frac{2}{3}\)

=> \(\frac{-7}{12}\)< \(\frac{3.\left(x-1\right)}{12}\)< \(\frac{8}{12}\)

=> 3 . ( x - 1 ) thuộc { - 6 ; - 5 ; - 4 ; - 3 ; - 2 ; - 1 ; 0 ; 1 ; 2 ; 3 ; 4 ; 5 ; 6 ; 7}

Lập bảng tính giá trị x , cái này dễ lên bạn tự làm nha

1/ \(-\frac{7}{12}< \frac{x-1}{4}< \frac{2}{3}\)

hay \(\frac{-7}{12}< \frac{3.\left(x-1\right)}{12}< \frac{8}{12}\)

Vậy \(-7< 3.\left(x-1\right)< 8\)

Vậy \(3.\left(x-1\right)\in\left\{-6;-5;-4;...;7\right\}\)

mà \(x\in Z\)nên \(3.\left(x-1\right)⋮3\)

Vậy \(3.\left(x-1\right)\in\left\{-6;-3;0;3;6\right\}\)

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

tới đây dễ rồi thì làm nốt nhé, để thời gian làm mấy câu sau!

\(\left(\frac{1}{2}+\frac{3}{4}-\frac{1}{3}\right):\frac{-5}{6}< x< \frac{4}{21}.\frac{4}{7}\)

\(\Rightarrow\left(\frac{6}{12}+\frac{9}{12}-\frac{4}{12}\right):\frac{-10}{12}< x< \frac{16}{147}\)

\(\Rightarrow\frac{11}{12}.\frac{-12}{10}< x< \frac{16}{147}\)

\(\Rightarrow\frac{-11}{10}< x< \frac{16}{147}\)

\(\Rightarrow\frac{-1617}{1470}< x< \frac{16}{1470}\)

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