(x-5)/(x+2)≥1,
(x-5)/(x+2)-1≥0,
(x-5-x-2)/(x+2)≥0,
-7/(x+2)≥0. For this inequality to be true the fraction has to be positive. Since the numerator is always negative, the denominator must also be negative, that is, x+2<0, x<-2. At x=-2 the fraction becomes indefinitely positive (+∞). Solving for x in interval form we have x∈(-∞,-2]. In other words, at x=-2, the fraction is infinitely greater than 1, and for x<-2 it's definitely positive.