#### Answer

$\left( \dfrac{3}{2},\infty \right]$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given inequality, $
\dfrac{6x+3}{-4} \lt -3
,$ 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 $\ge.$
$\bf{\text{Solution Details:}}$
Multiplying both sides by a negative number (and consequently reversing the sign), the inequality above is equivalent to
\begin{array}{l}\require{cancel}
-4\left(\dfrac{6x+3}{-4}\right) \gt -4(-3)
\\\\
6x+3 \gt 12
.\end{array}
Using the properties of inequality, the inequality above is equivalent to
\begin{array}{l}\require{cancel}
6x \gt 12-3
\\\\
6x \gt 9
\\\\
x \gt \dfrac{9}{6}
\\\\
x \gt \dfrac{3}{2}
.\end{array}
In interval notation, the solution set is $
\left( \dfrac{3}{2},\infty \right]
.$