Answer
$x=\left\{ 3,5 \right\}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given equation, $
5|x-4|=5
,$ use the properties of equality to isolate the absolute value expression. Then use the definition of absolute value equality. Use the properties of equality to isolate the variable.
$\bf{\text{Solution Details:}}$
Using the properties of equality to isolate the absolute value expression results to
\begin{array}{l}\require{cancel}
|x-4|=\dfrac{5}{5}
\\\\
|x-4|=1
.\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}
x-4=1
\\\\\text{OR}\\\\
x-4=-1
.\end{array}
Solving each equation results to
\begin{array}{l}\require{cancel}
x-4=1
\\\\
x=1+4
\\\\
x=5
\\\\\text{OR}\\\\
x-4=-1
\\\\
x=-1+4
\\\\
x=3
.\end{array}
Hence, $
x=\left\{ 3,5 \right\}
.$