Answer
The solution set is $\left\{ x|x\ge -5 \right\}$.
Work Step by Step
So, the inequality can be solved as follows:
$\begin{align}
& \frac{2x-3}{8}\le \frac{3x}{8}+\frac{1}{4} \\
& \frac{2x-3}{8}\le \frac{3x}{8}+\frac{2}{8}\text{ Make the denominator the same on both sides} \\
& \left( \frac{2x-3}{8} \right)\times 8\le \frac{3x}{8}\times 8+\frac{2}{8}\text{ }\times \text{8 Multiply both sides by 8} \\
& 2x-3\le 3x+2\text{ } \\
& 2x-3+3\le 3x+2+3\text{ Add 3 on both sides } \\
& 2x\le 3x+5\text{ } \\
& 2x-3x\le 3x+5-3x\text{ Subtract 3}x\text{ from both sides } \\
& -x\le 5\text{ }
\end{align}$
Therefore, the solution of the inequality is
$\begin{align}
& -x\le 5 \\
& x\ge -5
\end{align}$
