\(\dfrac{4x-3}{x-1}< 5\)
\(\Leftrightarrow4x-3< 5\left(x-1\right)\)
\(\Leftrightarrow4x-3< 5x-5\)
\(\Leftrightarrow4x-3-5x+5< 0\)
\(\Leftrightarrow-x+2< 0\)
\(\Leftrightarrow-x< -2\)
\(\Leftrightarrow x>2\)
Vậy x > 2
\(\dfrac{4X-3}{X-1}< 5\Leftrightarrow\dfrac{4X-3}{X-1}-5< 0\Leftrightarrow\dfrac{4X-3-5X+5}{X-1}< 0\)
\(\Leftrightarrow\dfrac{-X+2}{X-1}< 0\Leftrightarrow\left[{}\begin{matrix}-x+2>0\\-x+2< 0\end{matrix}\right.\) và \(\left[{}\begin{matrix}x-1< 0\\x-1>0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x< 2\\x>2\end{matrix}\right.\) và \(\Leftrightarrow\left[{}\begin{matrix}x< 1\\x>1\end{matrix}\right.\)
\(\dfrac{4x-3}{x-1}< 5\\ \Leftrightarrow4x-3< 5\left(x-1\right)\\ \Leftrightarrow4x-3< 5x-1\\ \Leftrightarrow4x-3-5x+1< 0\\ \Leftrightarrow-x-2< 0\\ \Leftrightarrow-x< 2\\ \Leftrightarrow x< -2\)
Vậy........................................
\(\dfrac{4x-3}{x-1}< 5\\ \Leftrightarrow4x-3< 5\left(x-1\right)\\ \Leftrightarrow4x-3< 5x-5\\ \Leftrightarrow4x-3-5x+5< 0\\ \Leftrightarrow-x+2< 0\\ \Leftrightarrow-x< -2\\ \Leftrightarrow x< 2\\ \text{ Vậy }x< 2\)
