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Are these 2 sentences the same?

We can use our equity to finance our project.

We can finance our project by using our equity.

So is this formula always right in all situations?:

to do thing 1 in order to do thing 2 = to do thing 2 by doing thing 1

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The two sentences are effectively equivalent and interchangeable in most contexts. They describe identical facts, but the subtle differences in structure could be used to emphasize different aspects of the situation.

The first sentence could be elaborated as:

We have the ability to use our equity. We will use that ability to finance our project.

The second sentence could be elaborated as:

We have the ability to finance our project. We will accomplish this goal by using our equity.

The first sentence might be an answer to "What can we do with our equity?"

The second sentence might be an answer to "How can we finance our project?"

However, as both sentences present the same facts, either sentence really could be used to answer either question.

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