How do you solve #(-x+8)/(x-2)>=5# using a sign chart?

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Answer 1 · 2017-08-22T12:43:22

Solution: #2< x <=3 or (2, 3]#

#(-x+8)/(x-2) >=5 or (-x+8)/(x-2)-5 >=0 # or

# (-x+8-5x+10)/(x-2) >=0 or (-6x +18)/(x-2) >=0 # or

# (-6(x-3)) /(x-2) >= 0 or (x-3)/(x-2) <=0 # Critical points are

#x=2 , x=3# When #x =3 ; (x-3)/(x-2) =0 ; x !=2#

Sign chart:

when # x <2# ; sign of #(x-3)/(x-2) # is #(-)/(-)=(+) ; >0 #

when #2< x <3# ; sign of #(x-3)/(x-2) # is #(-)/(+)=(-) ; < 0 #

when # x > 3# ; sign of #(x-3)/(x-2) # is #(+)/(+)=(+) ; >0 #

Solution: #2< x <=3 or (2, 3]# [Ans]