#### Answer

$x=\left\{ -1,5 \right\}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given equation, $
|2-x|-3=0
,$ use the properties of equality to isolate the absolute value expression. Then use the definition of absolute value equality.
$\bf{\text{Solution Details:}}$
Using the properties of equality, the equation above is equivalent to
\begin{array}{l}\require{cancel}
|2-x|=3
.\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}
2-x=3
\\\\\text{OR}\\\\
2-x=-3
.\end{array}
Solving each equation results to
\begin{array}{l}\require{cancel}
2-x=3
\\\\
-x=3-2
\\\\
-x=1
\\\\
x=-1
\\\\\text{OR}\\\\
2-x=-3
\\\\
-x=-3-2
\\\\
-x=-5
\\\\
x=5
.\end{array}
Hence, $
.$
Hence, the solutions are $
x=\left\{ -1,5 \right\}
.$