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lim as x→- ∞ (-5x/x-2)=-5

And I have to find the best interval of solutions for N

Relevant equations:

if x>N then |(-5x/x-2)-(-5)|<ε

My attempt:

|(-5x/x-2) - (-5)|<ε

|-10/x-2|<ε

x-2< 10/ε

as x→-∞ we can assume that x-2<0

x-2<10/ε

x< (10/ε)+2

therefore, the interval should be NE [(10/ε) +2, -∞)

however, the answer says that it should be -2 not +2. I don't know what I am doing wrong, if anyone can help that would be great! Thanks!