Question

Tìm x biết x thuộc Z

 

1/3 + 3/35 < x/210 < 4/7 + 3/5 + 1/3 5/3 + -14/3 < x > 8/5 + 18/101/2 + 3/4 + 5/6 < x > 3/2 + 5/4 + 7/6

Answer 1

Câu 1:

 \(\frac{1}{3}+\frac{3}{35}<\frac{x}{210}<\frac{4}{7}+\frac{3}{5}+\frac{1}{3}\)

\(\Rightarrow\frac{44}{105}<\frac{x}{210}<\frac{158}{105}\)

\(\Rightarrow\frac{88}{210}<\frac{x}{210}<\frac{316}{210}\)

\(\Rightarrow x\in\left\{89;90;91;92;...;310;311;312;313;314;315\right\}\)

Answer 2

Câu 3: 

\(\frac{5}{3}\)\(+\frac{-14}{3}\)\(<\)\(x\)\(<\)\(\frac{8}{5}+\frac{18}{10}\)

\(\Rightarrow\)\(-9\)\(<\)\(x\)\(<\)\(3,4\)

Mà \(x\in Z\)

\(\Rightarrow x\in\left\{-8;-7;-6;-5;...;1;2;3\right\}\)

Answer 3

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

\(\Rightarrow12x=36\)

\(\Rightarrow x=3\)

Answer 4

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