Question

Solve |5x - 1| < 1

x
x < 0 or x > 2/5
-2/5 < x < 2/5

Answer 1

`\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<(2)/(5)\\\\\boxed{\left\x\Big}\\\\\boxed{x\in\left(0,~~(2)/(5)\right)}`

Answer 2

1. 0 < x < 2/5

explanation: oddyseyware