The number of solution of the equation $| x - 9 | - | x + 2 | = - 5$ is

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Solution

$y = | x - 9 | - | x + 2 |$
Here the turning points are $- 2, 9$
$y = ⎧ ⎨ ⎩ \begin{matrix} - (x - 9) + (x + 2), & x < - 2 - (x - 9) - (x + 2), & - 2 \leq x < 9 (x - 9) - (x + 2), & x \geq 11 \end{matrix} \Rightarrow y = ⎧ ⎨ ⎩ \begin{matrix} 11, & x < - 2 7 - 2 x, & - 2 \leq x < 9 - 11, & x \geq 9 \end{matrix}$
Graph will be

Hence, the required number of solution is $1$ .

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