

If you divide an inequality by a negative number you have to flip the sign.
If you want to divide out the g before knowing if it’s positive or negative you need to make the case distinction.
If you make the case distinction and one branch results in a false statement (5 < 2 in this case), you have disproven the original inequality, or at least discovered a constraint on the original inequality. Then you arrive back at FooBarrington’s statement that includes the constraint :-)
Got bad news for you. They are starting in some places.
The Swiss public broadcaster shut down it’s FM channels at the turn of 2024 to 2025, at the end of next year all of the others have to shut down as well. It’s moving to DAB+ only, it’s a big pain for older cars.
I’ve heard Norway is even further along that route than Switzerland.