#### Answer

$\left[ -\dfrac{1}{2},\infty \right)$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given inequality, $
x-3(x+1)\le4x
,$ use the Distributive Property and 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 Distributive Property and the properties of inequality, the inequality above is equivalent to
\begin{array}{l}\require{cancel}
x-3(x)-3(1)\le4x
\\\\
x-3x-3\le4x
\\\\
x-3x-4x\le3
\\\\
-6x\le3
.\end{array}
Dividing both sides by a negative number (and consequently reversing the sign), the inequality above is equivalent to
\begin{array}{l}\require{cancel}
x\ge\dfrac{3}{-6}
\\\\
x\ge-\dfrac{1}{2}
.\end{array}
The red graph is the graph of the solution set.
In interval notation, the solution set is $
\left[ -\dfrac{1}{2},\infty \right)
.$