Answer
$\left( -\infty, -25 \right]
\cup
\left[ 15,\infty \right)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given inequality, $
|r+5|\ge20
,$ use the definition of absolute value inequalities. Then use the properties of inequality 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 $c\gt0$, $|x|\gt c$ implies $x\gt c \text{ or } x\lt-c$ (which is equivalent to $|x|\ge c$ implies $x\ge c \text{ or } x\le-c$), the inequality above is equivalent to
\begin{array}{l}\require{cancel}
r+5\ge20
\\\\\text{OR}\\\\
r+5\le-20
.\end{array}
Using the properties of inequality to isolate the variable results to
\begin{array}{l}\require{cancel}
r+5\ge20
\\\\
r\ge20-5
\\\\
r\ge15
\\\\\text{OR}\\\\
r+5\le-20
\\\\
r\le-20-5
\\\\
r\le-25
.\end{array}
In interval notation, the solution set is $
\left( -\infty, -25 \right]
\cup
\left[ 15,\infty \right)
.$
The colored graph is the graph of the solution set.