Question

Solve -7 - | x- 6| = - 12

Answer 1

`x=1\quad \mathrm{or}\quad \:x=11`

Explanation:

`-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\\(-\left|x-6\right|)/(-1)=(-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`

`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`

Answer 2

x=54/ 7 , 30/7

Explanation:

x=54/ 7 , 30/7