solve inequalite place in interval notation
4-x/x-6<=0
f(x)=(4-x)/(x-6)
First make a sketch of the equation (equality).
As x -> ± &infin, f(x) approaches -1.
There is also a vertical asymptote at x=6, approaching +∞ at 6- and -∞ at 6+. Therefore the function is discontinuous at that point.
The one zero is at x=4, where the function crosses from negative to positive.
If you have the sketch in front of you, it would be easy to find the places where the function is negative (≤0):
from -∞ to 4, and from 6+ to ∞.
If you need help putting that in interval notation, please post.