Question

The maximum number of values of $x$ if $|x-2|+|x-4|=2$ is

• A. $1$
• B. $2$
• C. $3$
• D. Infinitely many

Answer 1

The correct option is D Infinitely many

$|x-2|+|x-4|=2$

Case I:- $x<2$

$-(x-2)-(x-4)=2$

$\Rightarrow 2-x+4-x=2$

$\Rightarrow -2x=2-6$

$\Rightarrow x=\frac{-4}{-2}=2$

Case II:- $2\le x<4$

$(x-2)-(x-4)=2$

$x-2+4-x=2$

$\Rightarrow 2=2\Rightarrow$ For any value of $x$

Case III:- $x\ge 4$

$(x-2)+(x-4)=2$

$\Rightarrow 2x=2+6$

$\Rightarrow x=\frac{8}{2}=4$

Hence from the above $3$ case, $x$ can have infinitely many values.