#### Answer

$\text{Set Builder Notation: }
\left\{ x|x\gt-13 \right\}
\\\text{Interval Notation: }
\left( -13,\infty \right)$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
Use the properties of inequality to solve the given inequality, $
14x+9\gt13x-4
.$ 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}
14x+9\gt13x-4
\\\\
14x-13x\gt-4-9
\\\\
x\gt-13
.\end{array}
Hence, the solution set is
\begin{array}{l}\require{cancel}
\text{Set Builder Notation: }
\left\{ x|x\gt-13 \right\}
\\\text{Interval Notation: }
\left( -13,\infty \right)
.\end{array}