#### Answer

$x=-1$

#### Work Step by Step

Using the properties of equality, the solution to the given equation, $
\dfrac{3x-1}{5}+\dfrac{x+2}{2}=-\dfrac{3}{10}
$ is
\begin{array}{l}\require{cancel}
10\left( \dfrac{3x-1}{5}+\dfrac{x+2}{2} \right)=\left(-\dfrac{3}{10}\right)10
\\\\
2(3x-1)+5(x+2)=(-3)1
\\\\
6x-2+5x+10=-3
\\\\
6x+5x=-3+2-10
\\\\
11x=-11
\\\\
x=-\dfrac{11}{11}
\\\\
x=-1
.\end{array}