[tex]\displaystyle\\|5x-1|<1\\\\-1<5x-1<1\\\\\text{We have two inequalities}\\\\5x-1>-1~~~~~\text{and}~~~~~5x-1<1\\\\5x>-1+1~~~~~\text{and}~~~~~5x<1+1\\\\5x>0~~~~~\text{and}~~~~~5x<2\\\\x>0~~~~~\text{and}~~~~~x<\frac{2}{5}\\\\\boxed{\left\{x\Big|0 < x < \frac{2}{5}\right\}}\\\\\boxed{x\in\left(0,~~\frac{2}{5}\right)}[/tex]
