#### Answer

$\left[ 6,\infty \right)$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given inequality, $
-(9+x)-5+4x\ge4
,$ use the properties of inequality.
For the interval notation, use a parenthesis for the symbols $\lt$ or $\gt.$ Use a bracket for the symbols $\le$ or $\ge.$
For graphing inequalities, use a hollowed dot for the symbols $\lt$ or $\gt.$ Use a solid dot for the symbols $\le$ or $\ge.$
$\bf{\text{Solution Details:}}$
Using the properties of inequality, the inequality above is equivalent to
\begin{array}{l}\require{cancel}
-9-x-5+4x\ge4
\\\\
-x+4x\ge4+9+5
\\\\
3x\ge18
\\\\
x\ge\dfrac{18}{3}
\\\\
x\ge6
.\end{array}
The red graph is the graph of the solution set.
In interval notation, the solution set is $
\left[ 6,\infty \right)
.$