Question

Question #23a85

Answer 1

`|m-15|<4`

Explanation:

An absolute value inequality holds when a certain variable is bounded symmetrically with respect to zero, i.e. it ranges from `-k` to `k`, for some real number `k`.

For example. if you have `-8<x<8`, then you can say that `|x|<8`.

In your case, we need to subtract from all members a certain quantity, so that the foretold symmetry holds.

For example, if we subtract `11` from all sides, we have

`11-11<m-11<19-11`, and thus

`0<m-11<8`

From here, we can see that we need to subtract `4` more to make the range symmetric:

`-4<m-15<4`, and thus `|m-15|<4`