|3x - 2| - x > 1
+ Với \(x< \frac{2}{3}\) thì |3x - 2| - x = 2 - 3x - x = 2 - 4x > 1
=> 4x < 1
=> \(x< \frac{1}{4}\), thỏa mãn \(x< \frac{2}{3}\)
+ Với \(x\ge\frac{2}{3}\) thì |3x - 2| - x = 3x - 2 - x = 2x - 2 > 1
=> 2x > 3
=> \(x>\frac{3}{2}\), thỏa mãn \(x\ge\frac{2}{3}\)
Vậy \(\left[\begin{array}{nghiempt}x< \frac{1}{4}\\x>\frac{3}{2}\end{array}\right.\) thỏa mãn đề bài
Ta có:
\(\left|3x-2\right|-x>1\)
\(\Rightarrow\left|3x-2\right|>x+1\)
\(\Rightarrow\left[\begin{array}{nghiempt}3x-2>x+1\\3x-2< -\left(x+1\right)\end{array}\right.\)
\(\Rightarrow\left[\begin{array}{nghiempt}2x-3+x+1>x+1\\4x+\left(-x\right)-1-1< -x-1\end{array}\right.\)
\(\Rightarrow\left[\begin{array}{nghiempt}2x-3>0\\4x-1< 0\end{array}\right.\)
\(\Rightarrow\left[\begin{array}{nghiempt}2x>3\\4x< 1\end{array}\right.\)
\(\Rightarrow\left[\begin{array}{nghiempt}x>\frac{3}{2}\\x< \frac{1}{4}\end{array}\right.\)
Vậy \(\left[\begin{array}{nghiempt}x>\frac{3}{2}\\x< \frac{1}{4}\end{array}\right.\)