Answer
$\text{Set Builder Notation: }
\left\{ x|x\le-\dfrac{1}{10} \right\}
\\\text{Interval Notation: }
\left( -\infty,-\dfrac{1}{10} \right]$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the properties of inequality to solve the given inequality, $
-2x\ge\dfrac{1}{5}
.$ 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 $\ge.$
$\bf{\text{Solution Details:}}$
Dividing both sides by a negative number (and consequently reversing the inequality symbol), the inequality above is equivalent to
\begin{array}{l}\require{cancel}
-2x\ge\dfrac{1}{5}
\\\\
x\le\dfrac{\dfrac{1}{5}}{-2}
\\\\
x\le\dfrac{1}{5}\div-2
\\\\
x\le\dfrac{1}{5}\cdot\left(-\dfrac{1}{2} \right)
\\\\
x\le-\dfrac{1}{10}
.\end{array}
Hence, the solution set is
\begin{array}{l}\require{cancel}
\text{Set Builder Notation: }
\left\{ x|x\le-\dfrac{1}{10} \right\}
\\\text{Interval Notation: }
\left( -\infty,-\dfrac{1}{10} \right]
.\end{array}
