The distance between two real numbers is the absolute value of their difference,
. So the statement "all
that are 1/4 away from -6" is captured in the equation
or
To solve, you can use the definition of absolute value: if is not negative, then
; otherwise,
.
So there are two cases to consider:
1. Suppose . Then
, and the equation reduces to
2. Suppose . Then
and
, so the two solutions we found are correct because both
and
are indeed 1/4 away from -6.
- - -
For the question regarding inequality, you know that the absolute value must return a non-negative number. In other words, there is no such that
.