Answer
$\left( \infty,-3 \right]$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given inequality, $
-5x-4\ge11
,$ 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 $\ge.$
$\bf{\text{Solution Details:}}$
Using the properties of inequality, the inequality above is equivalent to
\begin{array}{l}\require{cancel}
-5x\ge11+4
\\\\
-5x\ge15
.\end{array}
Dividing all sides by a negative number (and consequently reversing the sign), the inequality above is equivalent to
\begin{array}{l}\require{cancel}
x\le\dfrac{15}{-5}
\\\\
x\le-3
.\end{array}
In interval notation, the solution set is $
\left( \infty,-3 \right]
.$
