#### Answer

$\left( -\infty,28 \right)$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given inequality, $
-\dfrac{4}{7}x \gt -16
,$ use the Distributive property and the properties of inequality to isolate the variable.
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 to isolate the variable results to
\begin{array}{l}\require{cancel}
7\left( -\dfrac{4}{7}x \right) \gt 7(-16)
\\\\
-4x \gt -112
.\end{array}
Dividing by a negative number (and consequently reversing the sign), the inequality above is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{-4x}{-4} \lt \dfrac{-112}{-4}
\\\\
x \lt 28
.\end{array}
In interval notation, the solution set is $
\left( -\infty,28 \right)
.$
The colored graph is the graph of the solution set.