It means that you are supposed to prove something.
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It means give logical reasons for whatever you are trying to justify.
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To justify something in math is to prove it. Example: Justify 4x = 8 when x = 2. When x = 2, 4(2) = 8. Done. By doing this I justified that 4x = 8 when x = 2.
You sound like you're going to fail math this year and trying to justify it.
In math terms, it means to prove your answer and make sure it is right.