Answer
$x=7$
Work Step by Step
By cross-multiplication, the solution to the given equation, $
\dfrac{5x+3}{3x-7}=\dfrac{19}{7}
,$ is equivalent to
\begin{array}{l}\require{cancel}
7(5x+3)=19(3x-7)
\\\\
35x+21=57x-133
\\\\
35x-57x=-133-21
\\\\
-22x=-154
\\\\
x=\dfrac{-154}{-22}
\\\\
x=7
.\end{array}