Answer
$\left( -25,15 \right)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given inequality, $
|r+5| \lt 20
,$ use the definition of absolute value inequalities. Use the properties of inequalities to isolate the variable.
For the interval notation, use a parenthesis for the symbols $\lt$ or $\gt.$ Use a bracket for the symbols $\le$ or $\ge.$
For graphing inequalities, use a hollowed dot for the symbols $\lt$ or $\gt.$ Use a solid dot for the symbols $\le$ or $\ge.$
$\bf{\text{Solution Details:}}$
Since for any $c\gt0$, $|x|\lt c$ implies $-c\lt x\lt c$ (or $|x|\le c$ implies $-c\le x\le c$), the inequality above is equivalent to
\begin{array}{l}\require{cancel}
-20 \lt r+5 \lt 20
.\end{array}
Using the properties of inequality, the inequality above is equivalent to
\begin{array}{l}\require{cancel}
-20-5 \lt r+5-5 \lt 20-5
\\\\
-25 \lt r \lt 15
.\end{array}
In interval notation, the solution set is $
\left( -25,15 \right)
.$
The colored graph is the graph of the solution set.