Equivalent structure: I was so tired that I couldn't continue working

The question is that : rewrite this sentence with equivalent structure
“I was so tired that I couldn’t continue working”
My answer is that “I am that tired I couldn’t continue working”.
Is it correct?
By the way,I am wondering whether the following sentence exists or not.
“I am the last person + Ving…”. as we know “I am the last one + to V” but does the first sentence exist? If yes,how can I distinghuish them?

Your equivalent structure is not right, but I don’t understand the assignment. What is an ‘equivalent’ structure-- a similar structure (A) or a different structure (B) that expresses the statement similarly?

[i]I was so tired that I couldn’t continue working.

A. I was so exhausted that I had to stop working.
B. I was too tired to continue working[/i].

I am the last person living in this ghost town = I’m living here now.
I am the last person to live in this ghost town = I may or may not be living here now.


oh it means that the two stuctures have the same meaning. Looking the word “that” in the Longman dicionary,you can see it is said that “THAT (ADV) used to emphasize how much.” so are there any mistakes somewhere?

It is odd nowadays, and confusing in your sentence-- at least to me. Remember that your sentence also contains an elided ‘that’:

I am that tired that I couldn’t continue working.

I think it is usually a stand-alone structure, and uncommon:

I couldn’t continue working-- I was that tired!

thank you for your response!