28.6

Question

28.6<=F<=29.2 How to make this an absolute value inequality?

anonymous · Answer

If F is between those two numbers, then the difference between F and the average of those two numbers must be less than or equal to half the difference between those numbers.
In other words, you could express the interval [28.6,29.2] as 28.9 ± 0.3

Can you get it from there?

anonymous · Answer

I think I get your point. So if for example if it was 13 and 19, which the difference is 6, then F would be 3?

anonymous · Answer

No, the *absolute difference between the average of those two numbers and either one of those numbers is 3. So the difference between the average of those two numbers and F can't be more than 3.
(*=hint)

anonymous · Answer

What if it was the other way 'round? If you started with an absolute value inequality and wanted to put the solution as a compound inequality, how would you do it? Try working backwards from that model.

anonymous · Answer

That's what I have trouble doing. But let me think, would F=28.9 and then with it it would have either positive or negative 0.3?

anonymous · Answer

So it would be... $$lF-28.9l=0.3$$ Is this right or at least close?