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Solve for x and y

x=2y

5x<y+7

I said that the answer would be

y<7/9 and x<14/9

this is the right answer, but she asked how that works. How do both the equality and inequality hold true at the same time? Shouldn't the answer be undetermined? I don't quite know how to answer the question. My opinion is that as long as both x and y are less than their respective inequality, then the equality will then hold.

Are there any more precise thoughts or theories regarding the subject?