#### Answer

$x=\left\{ -8,14 \right\}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given equation, $
|x-3|=11
,$ 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 given equation is equivalent to
\begin{array}{l}\require{cancel}
x-3=11
\\\\\text{OR}\\\\
x-3=-11
.\end{array}
Solving each equation results to
\begin{array}{l}\require{cancel}
x-3=11
\\\\
x=11+3
\\\\
x=14
\\\\\text{OR}\\\\
x-3=-11
\\\\
x=-11+3
\\\\
x=-8
.\end{array}
Hence, $
x=\left\{ -8,14 \right\}
.$