#### Answer

$x=11$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given equation, $
\dfrac{1}{3}(2x-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}{3}(2x-1)=7
\\\\
3\cdot\dfrac{1}{3}(2x-1)=3\cdot7
\\\\
2x-1=21
\\\\
2x=21+1
\\\\
2x=22
\\\\
x=\dfrac{22}{2}
\\\\
x=11
.\end{array}
Checking: If $x=11,$ then
\begin{array}{l}\require{cancel}
\dfrac{1}{3}(2x-1)=7
\\\\
\dfrac{1}{3}(2\cdot11-1)=7
\\\\
\dfrac{1}{3}(22-1)=7
\\\\
\dfrac{1}{3}(21)=7
\\\\
7=7
\text{ (TRUE) }
.\end{array}
Hence, the solution is $
x=11
.$