Answer
$\left( 3,\infty \right)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given inequality, $
-(4+r)+2-3r\lt-14
,$ 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 Distributive Property and the properties of inequality, the inequality above is equivalent to
\begin{array}{l}\require{cancel}
-4-r+2-3r\lt-14
\\\\
-r-3r\lt-14+4-2
\\\\
-4r\lt-12
.\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}
r\gt\dfrac{-12}{-4}
\\\\
r\gt3
.\end{array}
The red graph is the graph of the solution set.
In interval notation, the solution set is $
\left( 3,\infty \right)
.$