Question

The solution set of the equation $| x -1|+| x |=2$ is

• A. a null set
• B. a singleton
• C. a set consisting of exactly two elements
• D. a set consisting of more than two elements

Answer 1

Answer: (C)

$|x-1|+|x|=2$
$\text { Case-1: } \text { If } x \in[0, \infty)$
$x-1+x=2 \Rightarrow x=3 / 2 \text { (solution) } $
$\text { Case-2: } \text { If } x \in[0,1)$
$ -x+1+x=2 \Rightarrow 1 \neq 2 \text { (no solution) } $
$\text { Case-3: } \text { If } x \in(-\infty, 0] $
$ -x+1-x=2 \Rightarrow x=\frac{-1}{2} \text { (solution) }$