Are these statements negated correctly using De Morgan's laws?

Question

$-10 < x < 2$.

Negation: $-10 \geq x$ or $x \geq 2$.

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$x \leq -1 \text{ or } x > 1$

Negation: $-1 > x \leq 1$

Answer 1

Once again, you are correct. Nice work. (You seem to have DeMorgan's "down-pat".)

I would simply have written the first negation like this:

$$x \leq -10\; \text{ or }\; x \geq 2$$

That's more a matter of preference, since $-10\geq x \equiv x\leq -10$.