Question

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

Answer 1

$y=|x-9|-|x+2|$
Here the turning points are $-2,9$
$y=\{\begin{array}{cc}-(x-9)+(x+2),& x<-2\\ -(x-9)-(x+2),& -2\le x<9\\ (x-9)-(x+2),& x\ge 11\end{array}\Rightarrow y=\{\begin{array}{cc}11,& x<-2\\ 7-2x,& -2\le x<9\\ -11,& x\ge 9\end{array}$
Graph will be


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