Answer
$\left[ -3,\infty \right)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given inequality, $
-2(x+4)\le6x+16
,$ 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}
-2(x)-2(4)\le6x+16
\\\\
-2x-8\le6x+16
.\end{array}
Using the properties of inequality, the inequality above is equivalent to
\begin{array}{l}\require{cancel}
-2x-6x\le16+8
\\\\
-8x\le24
.\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{24}{-8}
\\\\
x\ge-3
.\end{array}
The red graph is the graph of the solution set.
In interval notation, the solution set is $
\left[ -3,\infty \right)
.$
