#### Answer

$x=-1$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given equation, $
\dfrac{3x-1}{5}+\dfrac{x+2}{2}=-\dfrac{3}{10}
,$ multiply both sides by the $LCD.$ Then use the properties of equality to isolate the variable.
$\bf{\text{Solution Details:}}$
The $LCD$ of the denominators $\{
5,2,10
\}$ is $10$ since it is the smallest number which can be divided by all the denominators.
Multiplying both sides of the given equation by the $LCD=
10
$ results to
\begin{array}{l}\require{cancel}
2(3x-1)+5(x+2)=1(-3)
.\end{array}
Using the Distributive Property which is given by $a(b+c)=ab+ac,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
6x-2+5x+10=-3
.\end{array}
Using the properties of equality to combine like terms, the equation above is equivalent to
\begin{array}{l}\require{cancel}
6x+5x=-3+2-10
\\\\
11x=-11
\\\\
x=-\dfrac{11}{11}
\\\\
x=-1
.\end{array}