Calculate: 8-10x <-5+3x <= 10+2x

Expression: $8-10x < -5+3x \leq 10+2x$

Separate the compound inequality into two inequalities

$\begin{array} { l }-5+3x > 8-10x,\\-5+3x \leq 10+2x\end{array}$

Solve the inequality for $x$

$\begin{array} { l }x > 1,\\-5+3x \leq 10+2x\end{array}$

Solve the inequality for $x$

$\begin{array} { l }x > 1,\\x \leq 15\end{array}$

Find the intersection

$\begin{align*}&x \in \left\langle1, 15\right]\end{align*}$