Answer
$\text{Set Builder Notation: }
\left\{ x|x\lt30 \right\}
\\\text{Interval Notation: }
\left( -\infty,30 \right)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the properties of inequality to solve the given inequality, $
4\lt10-\dfrac{x}{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}
4\lt10-\dfrac{x}{5}
\\\\
\dfrac{x}{5}\lt10-4
\\\\
\dfrac{x}{5}\lt6
\\\\
5\left( \dfrac{x}{5} \right) \lt5(6)
\\\\
x\lt30
.\end{array}
Hence, the solution set is
\begin{array}{l}\require{cancel}
\text{Set Builder Notation: }
\left\{ x|x\lt30 \right\}
\\\text{Interval Notation: }
\left( -\infty,30 \right)
.\end{array}
