Answer
$\left( -\infty,\dfrac{7}{3} \right]$
Work Step by Step
Multiplying both sides by the $LCD=
10
$ and and using the properties of inequality, the solution to the given expression, $
\dfrac{x}{5}-\dfrac{3}{10}\ge\dfrac{x}{2}-1
,$ is
\begin{array}{l}\require{cancel}
2(x)-1(3)\ge5(x)-10(1)
\\\\
2x-3\ge5x-10
\\\\
2x-5x\ge-10+3
\\\\
-3x\ge-7
\\\\
x\le\dfrac{-7}{-3}
\\\\
x\le\dfrac{7}{3}
.\end{array}
Hence, the solution is $
\left( -\infty,\dfrac{7}{3} \right]
.$