Question

Giải bất phương trình

\(3\left|2x-1\right|\) < 2x+1

Answer 1

Có \(3\left|2x-1\right|< 2x+1\)

\(\Leftrightarrow\left[{}\begin{matrix}3\left(2x-1\right)>-\left(2x+1\right)\\3\left(2x-1\right)< 2x+1\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}6x-3>-2x-1\\6x-3< 2x+1\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}8x>2\\4x< 4\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x>\dfrac{1}{4}\\x< 1\end{matrix}\right.\)

\(\Leftrightarrow\dfrac{1}{4}< x< 1\)