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]

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