Answer
$\left\{ x|x\lt-\dfrac{2}{5} \right\}
\text{ or }
\left( -\infty, -\dfrac{2}{5} \right)
$
Work Step by Step
Using the properties of inequality, the given inequality, $
2(x+5)\lt8-3x
,$ is equivalent to
\begin{array}{l}\require{cancel}
2x+10\lt8-3x
\\\\
2x+3x\lt8-10
\\\\
5x\lt-2
\\\\
x\lt-\dfrac{2}{5}
.\end{array}
Hence, the solution is $
\left\{ x|x\lt-\dfrac{2}{5} \right\}
\text{ or }
\left( -\infty, -\dfrac{2}{5} \right)
.$
