Rewrite this equation in absolute value form: 18

Question

Rewrite this equation in absolute value form: 18<x<22
Thanks!

anonymous · Answer

Uh.. So much wrong with that..

Try:

|x - 20| < 2

anonymous · Answer

The distance between x and 20 is less than 2

anonymous · Answer

Thanks Polpak for the fast reply! But how did you get that?
Can you explain the process to me please? :)

anonymous · Answer

Yeah

You started with this:

18 < x < 22

Which means x is somewhere between 18 and 22. 

Smack dab in the middle of those two is 20, and the distance x can be from that central point is less than 2.

This is exactly what the absolute value expression:

|x - a| < b

means x is less than b units away from a.

Therefore |x - 20| < 2 is the inequality you're looking for.

anonymous · Answer

Oh I see!
Uhmm then is 60<x<70
|x-65|<5?

anonymous · Answer

Yep.

anonymous · Answer

awesome! Thanks so much!

anonymous · Answer

Of course! =)

anonymous · Answer

You can prove it also by going the other way:

$$|x - 65| < 5 \implies -5 < x-65 < 5$$

Add 65 to all three parts:

$$\implies 60 < x < 70$$

anonymous · Answer

Ohh okay! I shall use that now on to check my answers.
Thanks a bunch Polpak!