Question

solve (x-5)/(3-x)>=0

Answer 1

x>=5.

Answer 2

the top is 0 when x=5
the bottom is 0 when x=3


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3 5

we need to test the intervals:
(-inf,3);(3,5);(5,inf)

so if we plug in a number btw -inf and 3 like 0 we get
f(0)=(0-5)/(3-0)=-5/3 so this not bigger than 0

now we plug in number btw 3 and 5 like 4 and we get
f(4)=(4-5)/(3-4)=-1/(-1)=1 this is bigger than 0
so interval (3,5) is apart of our solution and don't forget we include 5 since it says =0
so actually we have (3,5]

last interval is (5,inf) we plug in number like 6 and we get
f(6)=(6-5)/(3-6)=1/(-3)=-1/3 not bigger than 0

so the solution is (3,5]