# Question #23a85

Oct 6, 2016

$| m - 15 | < 4$

#### 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 $| m - 15 | < 4$