Answer
$x=\left\{ -4,8 \right\}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given equation, $
|x-2|=6
,$ 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-2=6
\\\\\text{OR}\\\\
x-2=-6
.\end{array}
Solving each equation results to
\begin{array}{l}\require{cancel}
x-2=6
\\\\
x=6+2
\\\\
x=8
\\\\\text{OR}\\\\
x-2=-6
\\\\
x=-6+2
\\\\
x=-4
.\end{array}
Hence, $
x=\left\{ -4,8 \right\}
.$
