(-infinity,0] or (5,Infinity) as an inequality

Question

I would just like to know what this interval is a inequality

Answer 1

x ≤ 0 or 5 < x

Answer 2

There are 2 intervals in this problem.

 

(1) 

 

x ∈ (-∞,0] means that x ≤ 0

 

(2)

 

x ∈ (5,∞) means 5 < x < ∞

 

The word "or" means that x is in the union of these 2 intervals (if the problem said "and", x would be in the intersection of the 2 intervals).

 

x ∈ (-∞,0] ∪ (5,∞)