A. $|x|< 1 ⇒ x \in (-1, 1)$

B. $|x| ≤ 1 ⇒x \in [-1, 1]$

C. $|x-1|< 1⇒ x \in (0, 2)$

D. $|x-1| ≤1 ⇒x \in (0, 2]$

Choose the correct answer from the options given below :

A, B, C only

The correct answer is Option (2) → A, B, C only

A. $|x|< 1$

$⇒ -1<x<1$

$∴x \in (-1, 1)$

B. $|x| ≤ 1$

$⇒-1≤x≤1$

$∴x \in [-1, 1]$

C. $|x-1|< 1$

Case 1: $x≥1$

$x-1<1$

$x<2$

Case 2: $x<1$

$-x+1<1$

$-x<0$

$⇒x>0$

$∴x \in (0, 2)$