Answer
$\text{Set Builder Notation: }
\left\{ x|x\gt-\dfrac{9}{11} \right\}
\\\text{Interval Notation: }
\left( -\dfrac{9}{11},\infty \right)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the properties of inequality to solve the given inequality, $
4-8x\lt13+3x
.$ 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}
4-8x\lt13+3x
\\\\
-8x-3x\lt13-4
\\\\
-11x\lt9
.\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}
-11x\lt9
\\\\
x\gt\dfrac{9}{-11}
\\\\
x\gt-\dfrac{9}{11}
.\end{array}
Hence, the solution set is
\begin{array}{l}\require{cancel}
\text{Set Builder Notation: }
\left\{ x|x\gt-\dfrac{9}{11} \right\}
\\\text{Interval Notation: }
\left( -\dfrac{9}{11},\infty \right)
.\end{array}
