Take another look at the original sentence:

Sylvia shivered in her silk shirt, the difference in temperature between the hot road and the cold library was extreme.

You chose to fix it the correct way:

Sylvia shivered in her silk shirt, for the difference in temperature between the hot road and the cold library was extreme.

Sylvia shivered in her silk shirt is a main clause. The difference in temperature between the hot road and the cold library was extreme is a second main clause. Using a comma and a coordinating conjunction like for is an excellent way to fix the problem.

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