Multiply both sides by (x-5)(x-6) This will get rid of the fractions.
# (x-5)(x-6)xx -10/(x-5) >= (x-5)(x-6) xx -11/(x-6)# This gives
# (x-6) xx -10 >= (x-5) xx -11# multiplying across the ( ) gives
# - 10x + 60 >= -11 x + 55 # adding + 10x to both sides gives
# -10x + 10 x + 60 >= - 11x + 10 x + 55 # resulting in
# + 60 >= -1 x + 55# subtract 55 from both sides
# + 60 - 55 >= -1 x + 55 -55 # +5 resulting in
# + 5 >= -1 x# Now divide everything by -1
# + 5/-1 >=/-1 (-1x/-1)#
# +5/-1# = -5 the opposite of +5
# >=/-1# = #<=# The opposite of #>=#
# -1 x/-1# = + 1 x The opposite of -1 x so the answer is
# x >= -5#
