Answer
$r=\{ -29,7 \}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given equation, $
2|r+11|=36
,$ isolate first the absolute value expression. Then use the definition of absolute value equality. Do checking of the solution/s.
$\bf{\text{Solution Details:}}$
Using the properties of equality, the given equation is equivalent to
\begin{array}{l}\require{cancel}
2|r+11|=36
\\\\
|r+11|=\dfrac{36}{2}
\\\\
|r+11|=18
.\end{array}
Since for any $c\gt0$, $|x|=c$ implies $x=c \text{ or } x=-c,$ the equation above is equivalent to
\begin{array}{l}\require{cancel}
r+11=18
\\\\\text{OR}\\\\
r+11=-18
.\end{array}
Solving each equation results to
\begin{array}{l}\require{cancel}
r+11=18
\\\\
r=18-11
\\\\
r=7
\\\\\text{OR}\\\\
r+11=-18
\\\\
r=-18-11
\\\\
r=-29
.\end{array}
If $r=7,$ then
\begin{array}{l}\require{cancel}
2|r+11|=36?
\\\\
2|7+11|=36?
\\\\
2|18|=36?
\\\\
2(18)=36?
\\\\
36=36
\text{ (TRUE)}
.\end{array}
If $r=-29,$ then
\begin{array}{l}\require{cancel}
2|r+11|=36?
\\\\
2|-29+11|=36?
\\\\
2|-18|=36?
\\\\
2(18)=36?
\\\\
36=36
\text{ (TRUE)}
.\end{array}
Hence, $
r=\{ -29,7 \}
.$
