#### Answer

$\text{Set Builder Notation: }
\left\{ x|x\gt-6 \right\}
\\\text{Interval Notation: }
\left( -6,\infty \right)$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
Use the properties of inequality to solve the given inequality, $
3-4x\lt27
.$ Write the answer in both set-builder notation and interval notation.
$\bf{\text{Solution Details:}}$
Using the properties of inequality, the inequality above is equivalent to
\begin{array}{l}\require{cancel}
3-4x\lt27
\\\\
-4x\lt27-3
\\\\
-4x\lt24
.\end{array}
Dividing both sides by a negative number (and consequently reversing the inequality symbol), the inequality above is equivalent to
\begin{array}{l}\require{cancel}
-4x\lt24
\\\\
x\gt\dfrac{24}{-4}
\\\\
x\gt-6
.\end{array}
Hence, the solution set is
\begin{array}{l}\require{cancel}
\text{Set Builder Notation: }
\left\{ x|x\gt-6 \right\}
\\\text{Interval Notation: }
\left( -6,\infty \right)
.\end{array}