Question

The set of values of $x$, for which $|x-1|+|x+1|<4$ always holds true, is

• A. $(-2,2)$
• B. $(-\infty ,-2)\cup (2,\infty )$
• C. $(-\infty ,-1)\cup (1,\infty )$
• D. $(-2,-1)\cup (2,\infty )$

Answer 1

Answer: (A)

$(-2,2)$

$|x-1|+|x+1|<4$
Case $1.x<-1\Rightarrow 1-x-1-x<4\Rightarrow x>-2\Rightarrow x\in (-2,-1)$
Case $2.-1\le x<1\Rightarrow 1-x+x+1<4\Rightarrow 2<4\Rightarrow x\in [-1,1)$
Case $3.x\ge 1\Rightarrow x-1+x+1<4\Rightarrow x<2\Rightarrow x\in [1,2)$
Combining all the cases we get, $x\in (-2,2)$.