Answer
$\text{Set Builder Notation: }
\left\{ a|a\le-3.6 \right\}
\\\text{Interval Notation: }
\left(-\infty,-3.6 \right]$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the properties of inequality to solve the given inequality, $
9\le-2.5a
.$ Write the answer in both set-builder notation and interval notation. Finally, graph the solution set.
In the graph, a hollowed dot is used for $\lt$ or $\gt.$ A solid dot is used for $\le$ or $\ge.$
$\bf{\text{Solution Details:}}$
Using the properties of inequality, the given is equivalent to
\begin{array}{l}\require{cancel}
9\le-2.5a
\\\\
2.5a\le-9
\\\\
10(2.5a)\le10(-9)
\\\\
25a\le-90
\\\\
a\le-\dfrac{90}{25}
\\\\
a\le-\dfrac{18}{5}
\\\\
a\le-3.6
.\end{array}
Hence, the solution set is
\begin{array}{l}\require{cancel}
\text{Set Builder Notation: }
\left\{ a|a\le-3.6 \right\}
\\\text{Interval Notation: }
\left(-\infty,-3.6 \right]
.\end{array}
