Answer
$|m-1250|\le50$
Work Step by Step
Half-way between the given values, $
1200\text{ and } 1300
,$ is
\begin{array}{l}\require{cancel}
\dfrac{1200+1300}{2}
\\\\=
\dfrac{2500}{2}
\\\\=
1250
.\end{array}
The distance from $
1250
$ to $1200$ and $1300$ is $
50
.$
Since $|x|\lt c$ implies $-c\lt x\lt c$ (or $|x|\le c$ implies $-c\le x\le c$), then the given inequality, $
1200\le m \le1300
,$ is equivalent to
\begin{array}{l}\require{cancel}
|m-1250|\le50
.\end{array}
