Answer
$\text{Set Builder Notation: }
\left\{ t|t\le-12 \right\}
\\\text{Interval Notation: }
\left( -\infty,-12 \right]$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the properties of inequality to solve the given inequality, $
13\le-\dfrac{2}{3}t+5
.$ 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}
13\le-\dfrac{2}{3}t+5
\\\\
3(13)\le3\left( -\dfrac{2}{3}t+5 \right)
\\\\
39\le-2t+15
\\\\
2t\le15-39
\\\\
2t\le-24
\\\\
t\le-\dfrac{24}{2}
\\\\
t\le-12
.\end{array}
Hence, the solution set is
\begin{array}{l}\require{cancel}
\text{Set Builder Notation: }
\left\{ t|t\le-12 \right\}
\\\text{Interval Notation: }
\left( -\infty,-12 \right]
.\end{array}
