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 :
Answer & explanation
Correct answer: option 2
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: $x<1$
$-x+1<1$
$-x<0$
$⇒x>0$
$∴x \in (0, 2)$