Question

A phrase describing set of real numbers is given. Express the phrase as an inequality involving an absolute value.

All real numbers x less than 2 units from 4

Answer 1

The distance between \(x\) and \(4\) is \(|x-4|\)

Answer 2

More precisely.
If \(x\) is greater than \(4\), the distance is \(x-4\).
If \(x\) is less than \(4\), the distance is \(4-x\).
Both of these can be combined into \(|x-4|\).

Answer 3

Now for the distance to be less than \(2\) we need to put \(<2\).

Answer 4

So to combine them all you get \(|x-4|<2\).