if the inequality is: (x+5/x-2)>0 . "x-5 over x-2 greater or equal to 0". What would be the solution?

Question

a.(-infinity sign, -5] U (2, infinity sign)
b.(-5,2)
c.(-infinity sign, -5) U [2, infinity sign)
d.[-5,2]

My answer was C. Am I correct?

Answer 1

You are looking for those values of x, so that
y = (x+5)/(x-2) lies above the x-axis

first of all, x ≠ 2 or else we are dividing by zero

critical values are -5 and 2
investigate x < -5, say x = -10
then y = -/- = + , that's good
investigate between -5 and 2, say x = 0
y = +/2 < 0 , no good
investigate x > 2 , say x = 5
y = +/+ > 0 , that's good

in my notation:
x< -5 OR x > 2

I will let you sort it out with the new-fangled notation.