#### Answer

$x= \left\{ \dfrac{1}{5}, 7 \right\}$

#### Work Step by Step

Since for any $a\gt0$, $|x|=a$ implies $x=a$ or $x=-a$, then the solution/s to the given equation, $
\left| \dfrac{2x+3}{3x-4} \right|=1
,$ is/are
\begin{array}{l}\require{cancel}
\dfrac{2x+3}{3x-4}=1
\\\\
2x+3=1(3x-4)
\\\\
2x+3=3x-4
\\\\
2x-3x=-4-3
\\\\
-x=-7
\\\\
x=7
\\\\\text{OR}\\\\
\dfrac{2x+3}{3x-4}=-1
\\\\
2x+3=-1(3x-4)
\\\\
2x+3=-3x+4
\\\\
2x+3x=4-3
\\\\
5x=1
\\\\
x=\dfrac{1}{5}
.\end{array}
Hence, the solutions are $
x= \left\{ \dfrac{1}{5}, 7 \right\}
.$