|X-8|is greater than but equal to 3...solve

Answer 1

|x-8| >= 3

so, either
(x-8) >= 3 if (x-8) >= 0
or
-(x-8) >= 3 if (x-8) < 0

x-8 >= 3 means x>=11
since we require x-8>=0, that's ok

-(x-8) >= 3 means
-x+8 >= 3
x <= -5
since we require x-8<0, that's ok

final answer: x <= -5 or x >= 11

Think of the shape of the graph. It looks like a V. Requiring that |x-8|>=3 means you get the two branches of the V above the line y=3.