Answer
$\text{Set Builder Notation: }
\left\{ x|x\le-8 \right\}
\\\text{Interval Notation: }
\left( -\infty,-8 \right]$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the properties of inequality to solve the given inequality, $
7\le1-\dfrac{3}{4}x
.$ 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}
7\le1-\dfrac{3}{4}x
\\\\
4(7)\le4\left( 1-\dfrac{3}{4}x \right)
\\\\
28\le4-3x
\\\\
3x\le4-28
\\\\
3x\le-24
\\\\
x\le-\dfrac{24}{3}
\\\\
x\le-8
.\end{array}
Hence, the solution set is
\begin{array}{l}\require{cancel}
\text{Set Builder Notation: }
\left\{ x|x\le-8 \right\}
\\\text{Interval Notation: }
\left( -\infty,-8 \right]
.\end{array}
