Question 772506
Treat the |x-4| as the variable and first solve for that.  THEN examine the two conditions, {{{x-4<0}}}, and {{{x-4>=0}}} and solve each of these conditions separately.  Note, "conditions", are NOT the equations for you to solve; they are possibilities about x-4.





After further thinking knowing that this stuff is often complicated for people, here is more help, steps.


{{{3*abs(x-4)=24+9}}}
{{{3*abs(x-4)=33}}}
{{{abs(x-4)=11}}}   after dividing both sides by 3,

and now the conditions to check:


CONDITION:
{{{x-4<0}}}, {{{abs(x-4)=4-x}}}
{{{abs(x-4)=11}}}
{{{4-x=11}}}
{{{-x=11-4}}}
{{{x=-7}}}__________part of the answer


CONDITION:
{{{x-4>=0}}}, {{{abs(x-4)=x-4}}}
{{{abs(x-4)=11}}}
{{{x-4=11}}}
{{{x=11+4}}}
{{{x=15}}}________other part of answer