Sufficient condition for 3 positive scales to represent sides of a triangle

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Now with the above condition check the following video at 4:00 Check https://youtu.be/Zlnpo3GxWpY?si=Pagh6pcxgmRmEUHy

At 4:00

Any one of the inequalities (written with red color) should be sufficient for us to find the required sample space but it leads to the wrong answer (also clearly using only one of those inequalities as a sufficient condition leads to 2 answers) thus the condition on 3 positive scales which I found must be wrong but I'm unable to find my mistake in it please help