#### Answer

$x=\{ 5,11 \}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given equation, $
|x-8|=3
,$ use the definition of an absolute value equality. Then use the properties of equality to isolate the variable.
$\bf{\text{Solution Details:}}$
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}
x-8=3
\\\\\text{OR}\\\\
x-8=-3
.\end{array}
Using the properties of equality to isolate the variable in each equation results to
\begin{array}{l}\require{cancel}
x-8=3
\\\\
x=3+8
\\\\
x=11
\\\\\text{OR}\\\\
x-8=-3
\\\\
x=-3+8
\\\\
x=5
.\end{array}
Hence, $
x=\{ 5,11 \}
.$