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when you have > or < and multiply/divide by a negative number the sign inverts because given 2 positive numbers a and b it's easy to see that |a|>|b| if and only if a>b, but given two negative numbers x and y it's also easy to see that |x|>|y| if and only if x<y, try and example: for positive numbers 4 and 5, |5|>|4| and 5>4 but with negatives -5 and -4: |-5|>|-4| and -4>-5.

but this affects in no way the = sign because in the equality we don't have a term bigger than the other... it's like "both sides had the same value"

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Q: Why does an equal sign stay the same with multiplying or dividing negative numbers?
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