Either Works

"x is less than -2 or x is greater than 3" is a different kind of compound inequality. A number is a solution if it satisfies either condition. It does not need to satisfy both. No number is below -2 and above 3 at the same time, so no number could satisfy both. The solutions are two separate rays on the number line, pointing away from each other:

x < -2 or x > 3: two rays, nothing between them

"And" means both conditions must hold, so the solutions are the numbers in both sets. These numbers are called the overlap. "Or" means either condition may hold, so the solutions are the numbers in at least one of the sets. These numbers are called the union. In these examples, the overlap is a segment and the union is two rays. Other pairs of conditions can give other shapes.

An "or" inequality cannot be written as a chain, because a chain means both conditions hold. So x < -2 or x > 3 stays as two inequalities joined by the word "or".