Giá trị x thuộc Z thỏa mãn 1/2 - (1/3 + 3/4) < = x < = 1/24 - (1/8 - 1/3) là:

6/30

Giá trị \(x \in \mathbb{Z}\) thoả mãn \(\frac{1}{2} - \left( {\frac{1}{3} + \frac{3}{4}} \right) \le x \le \frac{1}{{24}} - \left( {\frac{1}{8} - \frac{1}{3}} \right)\) là:

x = −1;

x = 0;

x = −1 hoặc x = 0;

x = 1;

Giải thích

Đáp án đúng là: B.

\(\frac{1}{2} - \left( {\frac{1}{3} + \frac{3}{4}} \right) \le x \le \frac{1}{{24}} - \left( {\frac{1}{8} - \frac{1}{3}} \right)\)

\(\frac{1}{2} - \left( {\frac{4}{{12}} + \frac{9}{{12}}} \right) \le x \le \frac{1}{{24}} - \left( {\frac{3}{{24}} - \frac{8}{{24}}} \right)\)

\(\frac{1}{2} - \frac{{13}}{{12}} \le x \le \frac{1}{{24}} - \frac{{ - 5}}{{24}}\)

\(\frac{6}{{12}} - \frac{{13}}{{12}} \le x \le \frac{1}{{24}} + \frac{5}{{24}}\)

\(\frac{{ - 7}}{{12}} \le x \le \frac{6}{{24}}\)

\(\frac{{ - 7}}{{12}} \le x \le \frac{1}{4}\)

Ta có \(\frac{{ - 12}}{{12}} < \frac{{ - 7}}{{12}} \le x \le \frac{1}{4} < \frac{4}{4}\)

Hay \( - 1 < \frac{{ - 7}}{{12}} \le x \le \frac{1}{4} < 1\)

Do đó giá trị x nguyên thoả mãn là x = 0.