Question

bài 1 : Tìm x thuộc Z, biết

1) \(\frac{-5}{6}.\frac{120}{25}< x< \frac{-7}{15}.\frac{9}{14}\)                                                                       2) \(\left(\frac{-5}{3}\right)^3< x< \frac{-24}{35}.\frac{-5}{6}\)

Answer 1

1) \(\frac{-5}{6}.\frac{120}{25}< x< \frac{-7}{15}.\frac{9}{14}\)

\(\Leftrightarrow\frac{-5}{6}.\frac{24}{5}< x< \frac{-63}{210}\)

\(\Leftrightarrow-40< x< \frac{-63}{210}\)

\(\Leftrightarrow\frac{-400}{10}< \frac{10x}{10}< \frac{-3}{10}\)

\(\Leftrightarrow-400< 10x< -3\)

\(\Leftrightarrow x\in\left\{-39;-38;...;-2;-1\right\}\)

2) \(\left(\frac{-5}{3}\right)^3< x< \frac{-24}{35}.\frac{-5}{6}\)

\(\Leftrightarrow\frac{-125}{25}< x< \frac{4}{7}\)

\(\Leftrightarrow\frac{-35}{7}< \frac{-7x}{7}< \frac{4}{7}\)

\(\Leftrightarrow-35< -7x< 4\)

\(\Leftrightarrow x\in\left\{4;3;2;1;0\right\}\)