Answer
$(-\infty, -40)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given inequality, $
-\dfrac{3}{4}x\ge30
,$ use the properties of inequality.
For the interval notation, use a parenthesis for the symbols $\lt$ or $\gt.$ Use a bracket for the symbols $\le$ or $\ge.$
For graphing inequalities, use a hollowed dot for the symbols $\lt$ or $\gt.$ Use a solid dot for the symbols $\le$ or $\ge.$
$\bf{\text{Solution Details:}}$
Using the properties of inequality, the inequality above is equivalent to
\begin{array}{l}\require{cancel}
4\left(-\dfrac{3}{4}x\right)\ge4(30)
\\\\
-3x\ge120
.\end{array}
Dividing both sides by a negative number (and consequently reversing the sign), the inequality above is equivalent to
\begin{array}{l}\require{cancel}
x\le\dfrac{120}{-3}
\\\\
x\le-40
.\end{array}
The red graph is the graph of the solution set.
In interval notation, the solution set is $
(-\infty, -40)
.$