Question

Number of solution(s) of equation $|x-1|-|x-2|=10$ is

• A. $0$
• B. $1$
• C. $2$
• D. $4$

Answer 1

The correct option is A $0$

$|x-1|-|x-2|=10$
Critical points are $x=1,2$

Case-$1:x\le 1$
$\Rightarrow -(x-1)-(-(x-2\left)\right)=10\Rightarrow -x+1+x-2=10$
$\Rightarrow -1=10$ (not possible)

Case-$2:1<x<2$
$\Rightarrow (x-1)-(-(x-2\left)\right)=10\Rightarrow x-1+x-2=10$
$\Rightarrow x=\frac{13}{2}\notin (1,2)$

Case-$3:x\ge 2$
$\Rightarrow (x-1)-(x-2)=10$
$\Rightarrow 1=10$ (not possible)

So the equation has no solution.