Answer
$\left\{ x|x\le-10.875 \right\}
\text{ or }
\left( -\infty, -10.875 \right]
$
Work Step by Step
Using the properties of inequality, the given inequality, $
0.7(2+x)\ge1.1x+5.75
,$ is equivalent to
\begin{array}{l}\require{cancel}
1.4+0.7x\ge1.1x+5.75
\\\\
0.7x-1.1x\ge5.75-1.4
\\\\
-0.4x\ge4.35
\\\\
x\le\dfrac{4.35}{-0.4}
\\\\
x\le-10.875
.\end{array}
Hence, the solution is $
\left\{ x|x\le-10.875 \right\}
\text{ or }
\left( -\infty, -10.875 \right]
.$