First, subtract #color(red)(5)# from each side of the inequality to isolate the absolute value function:
#abs(5 - x) + 5 - color(red)(5) >= 5 - color(red)(5)#
#abs(5 - x) + 0 >= 0#
#abs(5 - x) >= 0#
The absolute value function takes any term and transforms it to its non-negative form. Therefore, we must solve the term within the absolute value function for both its negative and positive equivalent.
#-0 >= 5 - x >= 0#
#0 >= 5 - x >= 0#
#-color(red)(5) + 0 >= -color(red)(5) + 5 - x >= -color(red)(5) + 0#
#-5 >= 0 - x >= -5#
#-5 >= -x >= -5#
#color(bue)(-1) xx -5 color(red)(<=) color(bue)(-1) xx -x color(red)(<=) color(bue)(-1) xx -5#
#5 color(red)(<=) x color(red)(<=) 5#
Or
#x >= 5# and #x <= 5#
Because #x# can be greater than or less than #5# and it can be equal to #5# the solution is #x# is the set of all Real Numbers: #{RR}#.
In other words, #x# can be any value and the inequality will be true.
The graph will look like a solid shaded area:
graph{x>=-10005}
