Answer:
[tex]x=1\quad \mathrm{or}\quad \:x=11[/tex]
Step-by-step explanation:
[tex]-7 - | x- 6| = - 12\\\\ \mathrm{Add\:}7\mathrm{\:to\:both\:sides}\\-7-\left|x-6\right|+7=-12+7\\\\Simplify\\-\left|x-6\right|=-5\\\\\mathrm{Divide\:both\:sides\:by\:}-1\\\frac{-\left|x-6\right|}{-1}=\frac{-5}{-1}\\\\Simplify\\\left|x-6\right|=5\\\\\mathrm{Apply\:absolute\:rule}:\\\quad \mathrm{If}\:|u|\:=\:a,\:a>0\:\mathrm{then}\:u\:=\:a\:\quad \mathrm{or}\quad \:u\:=\:-a\\\\x-6=-5\quad \mathrm{or}\quad \:x-6=5[/tex]
[tex]x-6=-5\quad :\quad x=1\\\\x-6=5\quad :\quad x=11\\\\\mathrm{Combine\:Solutions:}\\\\x=1\quad \mathrm{or}\quad \:x=11[/tex]
