Answer
$\left[ -12, \infty \right) $
Work Step by Step
Using $a(b+c)=ab+ac$ (or the Distributive Property), and using the properties of inequality, the solution to the given expression, $
-2(x+1)\le-x+10
,$ is \begin{array}{l}\require{cancel} -2x-2\le-x+10 \\\\ -2x+x\le10+2 \\\\ -x\le12 \\\\ x\ge-12 .\end{array} Hence, the solution is $ \left[ -12, \infty \right) .$