Answer
$\text{Set Builder Notation: }
\left\{ y|y\lt\dfrac{1}{16} \right\}
\\\text{Interval Notation: }
\left(-\infty,\dfrac{1}{16} \right)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the properties of inequality to solve the given inequality, $
-\dfrac{5}{8}\lt-10y
.$ 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}
-\dfrac{5}{8}\lt-10y
\\\\
10y\lt\dfrac{5}{8}
\\\\
y\lt\dfrac{\dfrac{5}{8}}{10}
\\\\
y\lt\dfrac{5}{8}\div10
\\\\
y\lt\dfrac{5}{8}\cdot\dfrac{1}{10}
\\\\
y\lt\dfrac{\cancel5}{8}\cdot\dfrac{1}{\cancel5(2)}
\\\\
y\lt\dfrac{1}{16}
.\end{array}
Hence, the solution set is
\begin{array}{l}\require{cancel}
\text{Set Builder Notation: }
\left\{ y|y\lt\dfrac{1}{16} \right\}
\\\text{Interval Notation: }
\left(-\infty,\dfrac{1}{16} \right)
.\end{array}