Answer
$\left( -\infty,5 \right)$
Work Step by Step
Using the properties of inequality, the given inequality, $
6-3(2-x)\lt2(1+x)+3
,$ simplifies to
\begin{array}{l}\require{cancel}
6-6+3x\lt2+2x+3
\\\\
3x\lt2x+5
\\\\
3x-2x\lt5
\\\\
x\lt5
.\end{array}
Hence, the solution is $
\left( -\infty,5 \right)
.$
