Let $\mathbb{R}$ form the D2010: Ordered vector space of real numbers.
Let $I \subseteq \mathbb{R}$ be a D1284: Real interval.
Let $c \in \mathbb{R}$.

Then

(1)	$I = (a, b) \quad \Rightarrow \quad I + c = (a + c, b + c)$
(2)	$I = [a, b) \quad \Rightarrow \quad I + c = [a + c, b + c)$
(3)	$I = (a, b] \quad \Rightarrow \quad I + c = (a + c, b + c]$
(4)	$I = [a, b] \quad \Rightarrow \quad I + c = [a + c, b + c]$