Question

If $|x-2|+|x-6|=3$ then the value of $x$ is

• A. $x\ge 6$
• B. $x\le 2$
• C. $2<x<6$
• D. No value for x

Answer 1

The correct option is D

No value for x

Given, $|x-2|+|x-6|=3$

For $x\le 2$

Changing the sign throughout , we have

$-(x-2)-(x-6)=3$

$-x+2-x+6=3$

$-2x+8=3$

$-2x=3-8$

$-2x=-5$

$\Rightarrow x=\frac{5}{2}$

This is not possible since $x\le 2$

For $x\ge 6$

$x-2+x-6=3$

$2x-8=3$

$2x=3+8$

$\Rightarrow x=\frac{11}{2}$

This is not possible since $x\ge 6$

Therefore no values for x which satisfy the given equation.