Bài 4:
a: \(\dfrac{2021}{2022}=1-\dfrac{1}{2022};\dfrac{2022}{2023}=1-\dfrac{1}{2023}\)
Ta có: 2022<2023
=>\(\dfrac{1}{2022}>\dfrac{1}{2023}\)
=>\(-\dfrac{1}{2022}< -\dfrac{1}{2023}\)
=>\(-\dfrac{1}{2022}+1< -\dfrac{1}{2023}+1\)
=>\(\dfrac{2021}{2022}< \dfrac{2022}{2023}\)
b: \(\dfrac{1001}{1000}=1+\dfrac{1}{1000};\dfrac{1002}{1001}=1+\dfrac{1}{1001}\)
mà \(\dfrac{1}{1000}>\dfrac{1}{1001}\)
nên \(\dfrac{1001}{1000}>\dfrac{1002}{1001}\)
Bài 6:
a: \(\dfrac{3}{8}< \dfrac{x}{4}< \dfrac{3}{4}\)
=>\(\dfrac{3}{8}< \dfrac{2x}{8}< \dfrac{6}{8}\)
=>3<2x<6
=>\(\dfrac{3}{2}< x< 3\)
mà x nguyên
nên x=2
b: \(\dfrac{-5}{8}< \dfrac{x}{6}< =-\dfrac{5}{10}\)
=>\(-\dfrac{5}{8}< \dfrac{x}{6}< =\dfrac{-1}{2}\)
=>\(\dfrac{-15}{24}< \dfrac{4x}{24}< =\dfrac{-12}{24}\)
=>-15<4x<=-12
=>\(-\dfrac{15}{4}< x< =-3\)
mà x nguyên
nên x=-3
c: \(\dfrac{5}{12}< \dfrac{x}{6}< \dfrac{3}{4}\)
=>\(\dfrac{5}{12}< \dfrac{2x}{12}< \dfrac{9}{12}\)
=>5<2x<9
=>\(\dfrac{5}{2}< x< \dfrac{9}{2}\)
mà x nguyên
nên \(x\in\left\{3;4\right\}\)
d: \(-\dfrac{11}{12}< \dfrac{x}{6}< \dfrac{1}{-2}\)
=>\(-\dfrac{11}{12}< \dfrac{2x}{12}< \dfrac{-6}{12}\)
=>-11<2x<-6
=>\(-\dfrac{11}{2}< x< -3\)
mà x là số nguyên
nên \(x\in\left\{-5;-4\right\}\)
