Giải:
a) \(\left|3x-1\right|< 5\)
\(\Leftrightarrow\left[{}\begin{matrix}3x-1< 5\\1-3x< 5\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}3x< 6\\-3x< 4\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x< 2\\x>-\dfrac{4}{3}\end{matrix}\right.\)
Vậy ...
b) \(\left|15x-1\right|>31\)
\(\Leftrightarrow\left[{}\begin{matrix}15x-1>31\\1-15x>31\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}15x>32\\-15x>30\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x>\dfrac{32}{15}\\x< -2\end{matrix}\right.\)
Vậy ...
a) | 3x - 1 | < 5
<=>\(\left[{}\begin{matrix}3x-1< 5\\3x-1>-5\end{matrix}\right.\)
<=>\(\left[{}\begin{matrix}3x>-4\\3x< 6\end{matrix}\right.\)
<=>\(\left[{}\begin{matrix}x>-\dfrac{4}{3}\left(loại\right)\\x< 2\left(nhân\right)\end{matrix}\right.\)
vậy x < 2
b) | 15x-1 | > 31
<=>\(\left[{}\begin{matrix}15x-1>31\\15x-1< -31\end{matrix}\right.\)
<=>\(\left[{}\begin{matrix}15x>32\\15x< -30\end{matrix}\right.\)
<=>\(\left[{}\begin{matrix}x>\dfrac{32}{15}\left(nhân\right)\\x< -6\left(loại\right)\end{matrix}\right.\)
vậy x > 32/15
