how do i write this in interval form??
(x+2)/(x-5)≤0
You should first note that .
Now we will have two alternatives, depending on whether the denominator is positive or negative...
Case 1: is positive, which means .
.
Case 2: is negative, which means .
.
It's pretty obvious that the ONLY which can not satisfy this equation are .
So the domain is .
Alternatively, it can be written or .
please be specific. are we talking about writing the domain in interval notation or the solution to the inequality in interval notation?
I suspect the latter. In which case set the numerator and denominator to zero. You get x = -2 or x = 5 (now note that x cannot be 5, because the denominator cannot in fact be zero, we just do this to figure out the signs). Now you can draw a number line and plot x = -2 and x = 5 on it. Then plug in numbers in each of the three intervals that you have. you will find that the middle interval is the only one that works. the resulting solution is