Question

Number of positive solutions of the equation $||x+1|-3|=5$ is

Answer 1

$||x+1|-3|=5$
$|x+1|-3=+5$ or
$|x+1|-3=-5$
case $1:|x+1|-3=+5$
$\Rightarrow |x+1|=8$
$\Rightarrow x+1=8\Rightarrow x=7$
or
$\Rightarrow x+1=-8\Rightarrow x=-9$

case $2:|x+1|-3=-5$
$\Rightarrow |x+1|=-2$ ,that is not possible
Hence, solution is $x=\{7,-9\}$
positive solution is $x=7$ (only one solution)