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)

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