#### Answer

$x\gt0$

#### Work Step by Step

Multiplying both sides by the $LCD=
10
$ and then using the properties of inequalities, the solution to the given inequality, $
\dfrac{x-1}{2}+\dfrac{x+3}{5}\gt\dfrac{1}{10}
,$ is
\begin{array}{l}\require{cancel}
5(x-1)+2(x+3)\gt1(1)
\\\\
5x-5+2x+6\gt1
\\\\
5x+2x\gt1+5-6
\\\\
7x\gt0
\\\\
x\gt\dfrac{0}{7}
\\\\
x\gt0
.\end{array}