Absolutely Absolute Absolutness

$\displaystyle |||||x-8| - 10| - 4| - 5 | - 1| = 0$

$\displaystyle \iff ||||x-8| - 10| - 4| - 5 | = 1$

$\displaystyle \iff |||x-8| - 10| - 4| = 6 \text{ or } 4$

$\displaystyle \iff ||x-8| - 10| = -2 , 10 , 0 \text{ or } 8$ , but $-2$ is discarded , obviously

$\displaystyle \iff |x-8| = 0, 20 , 10 , 2 \text{ or } 18$

$\displaystyle \iff x = 8 , -12 , 28 , -2 , 18 , 6 , 10 , -10 \text{ or } 26$ , i.e., there are $9$ possible values of $x$ .

$\large||x-8| -10|$ with $y=4$ marked in yellow.

$\Large| \large||x-8| -10|- 4\Large|$ with $y=5$ in yellow.

$\huge| \Large| \large||x-8| -10|- 4\Large| \large-5 \huge|$ with $y=1$ in yellow.

$\Huge| \huge| \Large| \large||x-8| -10|- 4\Large| \large-5 \huge| \large-1 \Huge|$