How do you solve #-10/(x-5)>=-11/(x-6)#?

1 Answer
Oct 2, 2016

Answer:

Get rid of the fractions and divide everything by a negative including the #>=# sign.

Explanation:

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#