Question

a)1/3+3/35<x/210<4/7+3/5+1/2

b)5/3+(-14/3)<x<8/5+18/10

Answer 1

a: \(\dfrac{1}{3}+\dfrac{3}{35}< \dfrac{x}{210}< \dfrac{4}{7}+\dfrac{3}{5}+\dfrac{1}{2}\)

\(\Leftrightarrow\dfrac{70}{210}+\dfrac{18}{210}< \dfrac{x}{210}< \dfrac{120}{210}+\dfrac{126}{210}+\dfrac{105}{210}\)

\(\Leftrightarrow88< x< 441\)

b: Ta có: \(\dfrac{5}{3}+\dfrac{-14}{3}< x< \dfrac{8}{5}+\dfrac{18}{10}\)

\(\Leftrightarrow\dfrac{5}{3}-\dfrac{14}{3}< x< \dfrac{8}{5}+\dfrac{9}{5}\)

=>-9/3<x<17/5

=>-3<x<3,4

mà x là số nguyên

nên \(x\in\left\{-2;-1;0;1;2;3\right\}\)