What is the difference? Which one is correct? What should be used where? What are the rules?

Congress is debating a bill requiring certain employers provide workers with unpaid leave so as to care for sick or newborn children.
The official answer is: to provide workers with unpaid leave so that they can

Several years ago the diet industry introduced a variety of appetite suppressants, but some of these drugs caused such severe stomach disorders as to be banned by the Food and Drug Administration.
The official answer is: such severe stomach disorders that they were

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Students in the metropolitan school district lack math skills to such a large degree as to make it difficult to absorb them into a city economy becoming ever more dependent on information-based industries.
The official answer is: are so lacking in math skills that it will be difficult to absorb them into a city economy becoming

The Emperor Augustus, it appears, commissioned an idealized sculptured portrait, the features of which are so unrealistic that they have constituted what one scholar calls an "artificial face"
The official answer is: so unrealistic as to constitute

Although one link in the chain was demonstrated to be weak, but not sufficiently so to require the recall of the automobile.
The official answer is: demonstrably weak, it was not so weak as to require