#### Answer

$x=-5$

#### Work Step by Step

Using the properties of equality, the solution to the given equation, $
\dfrac{3}{2}(2x+5)=-\dfrac{15}{2}
$, is
\begin{array}{l}
\dfrac{2}{3}\left[\dfrac{3}{2}(2x+5)\right]=-\dfrac{15}{2}\left[ \dfrac{2}{3}\right]
\\\\
2x+5=-5
\\\\
2x=-5-5
\\\\
2x=-10
\\\\
x=-\dfrac{10}{2}
\\\\
x=-5
.\end{array}
CHECKING:
\begin{array}{l}
\dfrac{3}{2}(2(-5)+5)=-\dfrac{15}{2}
\\\\
\dfrac{3}{2}(-10+5)=-\dfrac{15}{2}
\\\\
\dfrac{3}{2}(-5)=-\dfrac{15}{2}
\\\\
-\dfrac{15}{2}=-\dfrac{15}{2}
\text{ (TRUE)}
.\end{array}
Hence, the solution is $
x=-5
$.