#### Answer

$x=9$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given equation, $
\dfrac{1}{5}(4x-1)=7
,$ use the properties of equality to isolate the variable. Do checking of the solution.
$\bf{\text{Solution Details:}}$
Using the properties of equality to isolate the variable, the equation above is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{1}{5}(4x-1)=7
\\\\
5\cdot\dfrac{1}{5}(4x-1)=5\cdot7
\\\\
4x-1=35
\\\\
4x=35+1
\\\\
4x=36
\\\\
x=\dfrac{36}{4}
\\\\
x=9
.\end{array}
Checking: If $x=9,$ then
\begin{array}{l}\require{cancel}
\dfrac{1}{5}(4x-1)=7
\\\\
\dfrac{1}{5}(4\cdot9-1)=7
\\\\
\dfrac{1}{5}(36-1)=7
\\\\
\dfrac{1}{5}(35)=7
\\\\
7=7
\text{ (TRUE) }
.\end{array}
Hence, the solution is $
x=9
.$