Before arguing to me you should make sure that you have your facts straight.
Please be sure you have (your/the) facts straight before you make a decision.
In the above sentences is it correct to use 'your' or not?
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The idiom is "your facts straight". It does not mean that you own the facts. It means that you have verified the facts that you are asserting in your argument. In other words, they are "your facts" because they are the facts that you have chosen to make your argument.
Often we will make an argument based on facts that we remember. But sometimes we remember the facts incorrectly. If someone tells us to "get our facts straight" they are telling us either:
"Before you make this argument, check that the facts you are asserting are correct."
"I have heard your argument and it is incorrect because the facts you are asserting are incorrect. Go back and check your facts and come back with a new argument."