#### Answer

$\left[ -\dfrac{8}{9}, \infty \right)$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given inequality, $
11x\ge2(x-4)
,$ use the Distributive Property and the properties of inequality to isolate the variable.
$\bf{\text{Solution Details:}}$
Using the Distributive Property which is given by $a(b+c)=ab+ac,$ the inequality above is equivalent to
\begin{array}{l}\require{cancel}
11x\ge2(x)+2(-4)
\\\\
11x\ge2x-8
.\end{array}
Using the properties of inequality, the inequality above is equivalent to
\begin{array}{l}\require{cancel}
11x-2x\ge-8
\\\\
9x\ge-8
\\\\
x\ge-\dfrac{8}{9}
.\end{array}
Hence, the solution set is the interval $
\left[ -\dfrac{8}{9}, \infty \right)
.$