which natural english interpretation of this symbolic statement is correct? Part of Keith Devlin's Coursera MOOC on mathematical thinking requires  the translation of this symbolic statement into natural language:
$$ 5 < x < 7$$
Interpretation 1: $x$ is a single unknown number located somewhere between 5 and 7 on the number line.

Interpretation 2: x is an interval on the number line between 5 and 7. (a line segment).

Which interpretation is correct?
(I will define x to be a REAL NUMBER)

The first interpretation is correct.
For the second one, you would write
$$\{x\in \mathbb R ,\ 5<x<7\},$$
or simply
$$\{5<x<7\},$$
or (thanks to a comment) :
$$x\in(5,7).$$
