Can you negate comparisons by negating each individuals expression?

Question

For example the negation of $(expression1) < (expression2)$ is $ (expression1) >= (expression2)$ but can you say that the negation is: $not(expression1) < not(expression2)$? Similarly with other comparison operators like "="?

Answer 1

No: $3 < 3$ is false, but $-3 < -3$ is also false.