Question

Tìm tập hợp các số nguyên x thỏa mãn

a. \(3\frac{1}{3}:2\frac{1}{2}-1< x< 7\frac{2}{3}.\frac{3}{7}\)\(+\frac{5}{2}\)

b. \(\frac{1}{2}-\left(\frac{1}{3}+\frac{1}{4}\right)< x< \frac{1}{48}-\left(\frac{1}{16}-\frac{1}{6}\right)\)

Answer 1

                                                                 Bài giải

a, \(3\frac{1}{3}\text{ : }2\frac{1}{2}-1< x< 7\frac{2}{3}\cdot\frac{3}{7}+\frac{5}{2}\)

\(\frac{10}{3}\text{ : }\frac{5}{2}-1< x< \frac{23}{3}\cdot\frac{3}{7}+\frac{5}{2}\)

\(\frac{4}{3}-1< x< \frac{23}{7}+\frac{5}{2}\)

\(\frac{1}{3}< x< \frac{81}{14}\)

\(\Rightarrow\text{ }0,\left(3\right)< x< 5,78...\)

\(\Rightarrow\text{ }x\in\left\{1\text{ ; }2\text{ ; }3\text{ ; }4\text{ ; }5\right\}\)

b, \(\frac{1}{2}-\left(\frac{1}{3}+\frac{1}{4}\right)< x< \frac{1}{48}-\left(\frac{1}{16}-\frac{1}{6}\right)\)

\(\frac{1}{2}-\frac{7}{12}< x< \frac{1}{48}+\frac{5}{48}\)

\(-\frac{1}{12}< x< \frac{1}{8}\)

\(\Rightarrow\text{ }-0,08\left(3\right)< x< 0,125\)

\(\Rightarrow\text{ }x\in\varnothing\)