Question 770911
First, isolate the absolute value function.

{{{abs(x-5)=(9-3)/6}}}
{{{abs(x-5)=1}}}
The factor of 3 inside the absolute value function is positive; so inside or outside the absolute value, not important.


Now treat for conditions of {{{x-5<0}}} and {{{x-5>=0}}}
'
{{{x-5<0}}} means {{{abs(x-5)=-x-5=1}}}
{{{x+5=1}}}
{{{x=-4}}}
'
{{{x-5>=0}}} means {{{abs(x-5)=x-5=1}}}
{{{x=1+5}}}
{{{x=6}}}


RESULT: {{{highlight(x=-4)}}} OR {{{highlight(x=6)}}}