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

0

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1

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Solution

The correct option is A $0$
$| x - 1 | - | x - 2 | = 10$
Critical points are $x = 1, 2$

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

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

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

So the equation has no solution.

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