we have that
|x+6| >= 5
step 1
resolve for (x+6)>=5------> x>=5-6-------> x>= -1
the solution is the interval (-1, ∞)
step 2
resolve for -(x+6) >=5------> -x-6 >=5----> -x >= 5+6---> -x>=11----> x<=-11
the solution is the interval (-∞, -11)
using a graph tool
see the attached figure
the solution is the interval (-∞, -11) ∩ (-1, ∞)
