Câu 1:
\(\frac{1}{3}+\frac{3}{35}<\frac{x}{210}<\frac{4}{7}+\frac{3}{5}+\frac{1}{3}\)
\(\Rightarrow\frac{44}{105}<\frac{x}{210}<\frac{158}{105}\)
\(\Rightarrow\frac{88}{210}<\frac{x}{210}<\frac{316}{210}\)
\(\Rightarrow x\in\left\{89;90;91;92;...;310;311;312;313;314;315\right\}\)
Câu 3:
\(\frac{5}{3}\)\(+\frac{-14}{3}\)\(<\)\(x\)\(<\)\(\frac{8}{5}+\frac{18}{10}\)
\(\Rightarrow\)\(-9\)\(<\)\(x\)\(<\)\(3,4\)
Mà \(x\in Z\)
\(\Rightarrow x\in\left\{-8;-7;-6;-5;...;1;2;3\right\}\)
Câu 4:
\(\frac{1}{2}+\frac{3}{4}+\frac{5}{6}\)\(<\)\(x\)\(<\)\(\frac{3}{2}+\frac{5}{4}+\frac{7}{6}\)
\(\Rightarrow\frac{25}{12}\)\(<\)\(x\)\(<\)\(\frac{47}{12}\)
Nhân cả 3 vế với 12, ta có:
\(\Rightarrow\)\(25<12\)\(x<\)\(47\)
Từ 25 đến 47 có duy nhất số 36 chia hết cho 12
\(\Rightarrow12x=36\)
\(\Rightarrow x=3\)
