#### Answer

$(7,\infty)$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given inequality, $
3k+1\gt22
,$ 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}
3k\gt22-1
\\\\
3k\gt21
\\\\
k\gt\dfrac{21}{3}
\\\\
k\gt7
.\end{array}
The red graph is the graph of the solution set.
In interval notation, the solution set is $
(7,\infty)
.$