Answer
$\left\{x|x\gt 14\right\}$
Refer to the graph below.
Work Step by Step
Multiply $10$ to both sides to eliminate fractions:
\begin{align*}
\require{cancel}
10\left(\frac{2x-3}{5}+2\right)&\le 10\left(\frac{x}{2}\right)\\
10\left(\frac{2x-3}{5}\right)+10(2)&\le \cancel{10}^5\left(\frac{x}{\cancel{2}}\right)\\
\cancel{10}^2\left(\frac{2x-3}{\cancel{5}}\right)+20&\le 5x\\
2(2x-3)+20&\le 5x\\
4x-6+20&\le5x\\
4x+14&\le 5x\\
14&\le5x-4x\\
14&\le x\\
x&\ge 14\end{align*}
The solution set is $\left\{x|x\gt 14\right\}$.
To graph the solution set, plot a solid dot at $14$ and shade the region to its right.
Refer to the graph above.
