Solve:
#-9abs(x+8)+4<=-5#
Subtract #4# from both sides.
#-9abs(x+8)<=-5-4#
Simplify.
#-9abs(x+8)<=-9#
Divide both sides by #-9#. This will reverse the inequality.
#(color(red)cancel(color(black)(-9))^1abs(x+8))/color(red)cancel(color(black)(-9))^1>=color(red)cancel(color(black)(-9))^1/color(red)cancel(color(black)(-9))^1#
Simplify.
#abs(x+8)>=1#
Since #absa=+-a#, we can break the equation into two equations:
#x+8>=1# and #-(x+8)>=1#
Solve the first equation: #x+8>=1#.
Subtract #8# from both sides.
#x>=1-8#
Simplify.
#x>=-7#
Solve the second equation: #-(x+8)>=1#.
#-x-8>=1#
Add #8# to both sides.
#-x>=1+8#
Simplify.
#-x>=9#
Multiply both sides by #-1#. This will reverse the inequality.
#x>=9xx-1#
#x<=-9#
Solutions:
#x>=-7#
#x<=-9#
