I understand this question and Greg’s explanation in the video.

My question is shouldn’t this be |x| + |y| is less than or equal to 4?

I did the same thing as a Greg, but since the problem said less than 4 and not less than or equal to 4 my extreme cases were 3.99 and 0.01. And I made the problem too difficult for myself.

You’re right!! I saw this question and approached it the same way as Greg. Technically speaking, it should’ve been |x| + |y| <= 4 according to me.

Actually it doesn’t matter. The only difference is that the inequality becomes slack (<=) rather than strict (<), which means that the boundary is part of the area (and does not contribute to any of the area). The boundary is the same even with a (<), and there is no change in area as a result. The below is Desmos’ interpretation of |x| + |y| < 4:

It can also be 3.9999999999 and 0.000000001 after all. The use of a ‘<’ rather than a ‘<=’ doesn’t change the area in reality.

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This helps! Thank you so much!