Answer
$a=-4$
Work Step by Step
The absolute value of $x,$ written as $|x|,$ is the distance of $x$ from $0,$ and hence, is always a nonnegative number. Therefore, the left side of the given inequality, $
|a+4|\le0
,$ is always nonnegative. This means that the inequality is only satisfied when $|a+4|=0$ or when $a+4=0.$
Using the properties of equality to isolate the variable, the expression $a+4=0$ is equivalent to
\begin{array}{l}\require{cancel}
a+4=0
\\\\
a=-4
.\end{array}
In the graph, a hollowed dot is used for $\lt$ or $\gt.$ A solid dot is used for $\le$ or $\ge.$
