# Chapter 9 - Inequalities and Problem Solving - 9.3 Absolute-Value Equations and Inequalities - 9.3 Exercise Set: 64

$a=-4$

#### 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 $\ge.$

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