Answer
$\text{Set Builder Notation: }
\left\{ t|t\le-2 \right\}
\\\text{Interval Notation: }
\left( -\infty,-2 \right]$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the properties of inequality to solve the given inequality, $
4t+10\le2
.$ 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}
4t+10\le2
\\\\
4t\le2-10
\\\\
4t\le-8
\\\\
t\le-\dfrac{8}{4}
\\\\
t\le-2
.\end{array}
Hence, the solution set is
\begin{array}{l}\require{cancel}
\text{Set Builder Notation: }
\left\{ t|t\le-2 \right\}
\\\text{Interval Notation: }
\left( -\infty,-2 \right]
.\end{array}
