## College Algebra (11th Edition)

$x=-\dfrac{7}{3}$
$\bf{\text{Solution Outline:}}$ To solve the given inequality, $|3x+7|\le0 ,$ use the definition of absolute value to analyze the given inequality. $\bf{\text{Solution Details:}}$ The absolute value of $x$, given by $|x|,$ is the distance of $x$ from $0,$ and hence is always a nonnegative number. Therefore, for any $x,$ the expression at the left, $|3x+7| ,$ is nonnegative. The given inequality is satisfied only when $3x+7=0 .$ Using the properties of equality, then \begin{array}{l}\require{cancel} 3x+7=0 \\\\ 3x=-7 \\\\ x=-\dfrac{7}{3} .\end{array}