#### Answer

$\left( -\infty, -\dfrac{5}{2} \right]$

#### Work Step by Step

Using the properties of inequality, the given inequality, $
5x-(3+x)\ge2(3x+1)
,$ simplifies to
\begin{array}{l}\require{cancel}
5x-3-x\ge6x+2
\\\\
5x-x-6x\ge2+3
\\\\
-2x\ge5
\\\\
x\le\dfrac{5}{-2}
\\\\
x\le-\dfrac{5}{2}
.\end{array}
Hence, the solution is the interval $
\left( -\infty, -\dfrac{5}{2} \right]
.$