Question 789971
Most of these are almost the same format.
Treat the absolute value as a variable; you could also factor some of them.... actually you can factor ONE of them.  


Consider the possibility that the expression inside the absolute value can be positive, or less than or equal to zero.  Solve for each case.


For some expression |a-b|, 
if {{{a-b>=0}}} then |a-b|=a-b.
if {{{a-b<0}}} then |a-b|=-1(a-b)=b-a


Looking at your third sample,{{{abs(x-10)-4=2x}}}
{{{abs(x-10)=2x+4}}}
If {{{x-10>=0}}} then you have {{{x-10=2x+4}}}
{{{x-2x=10+4}}}
{{{-x=14}}}
{{{highlight(x=-14)}}}
If {{{x-10<0}}} then you have {{{-x+10=2x+4}}}
{{{-x-2x=-10+4}}}
{{{-3x=-6}}}
{{{highlight(x=2)}}}


Conclusion on this one is x is either 2 or -14.