Answer
$\text{Set Builder Notation: }
\left\{ x|x\le-1 \right\}
\\\text{Interval Notation: }
\left( -\infty,-1 \right]$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the properties of inequality to solve the given inequality, $
5-9x\ge19+5x
.$ 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}
5-9x\ge19+5x
\\\\
-9x-5x\ge19-5
\\\\
-14x\ge14
.\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}
-14x\ge14
\\\\
x\le\dfrac{14}{-14}
\\\\
x\le-1
.\end{array}
Hence, the solution set is
\begin{array}{l}\require{cancel}
\text{Set Builder Notation: }
\left\{ x|x\le-1 \right\}
\\\text{Interval Notation: }
\left( -\infty,-1 \right]
.\end{array}
