Answer
$\left[ -\dfrac{37}{3},\infty \right)$
Work Step by Step
Using the properties of inequality, the expression $
\dfrac{x+5}{5}-\dfrac{3+x}{8}\ge-\dfrac{3}{10}
$ simplifies to
\begin{array}{l}
40\left( \dfrac{x+5}{5}-\dfrac{3+x}{8} \right) \ge \left( -\dfrac{3}{10} \right)40\\\\
8(x+5)-5(3+x)\ge4(-3)\\
8x+40-15-5x\ge-12\\
3x+25\ge-12\\
3x\ge-37\\
x\ge-\dfrac{37}{3}
.\end{array}
In interval notation, the solution set is $
\left[ -\dfrac{37}{3},\infty \right)
$.
