#### Answer

$x=-\dfrac{7}{2}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given equation, $
|7+2x|=0
,$ use the properties of equality to solve for $7+2x=0.$
$\bf{\text{Solution Details:}}$
Since for any $c\ge0$, $|x|=c$ implies $x=c \text{ or } x=-c,$ the equation above is equivalent to
\begin{array}{l}\require{cancel}
7+2x=0
\\\\\text{OR}\\\\
7+2x=-0
.\end{array}
The equations above can be simplified to the single equation
\begin{array}{l}\require{cancel}
7+2x=0
.\end{array}
Using the properties of equality to isolate the variable results to
\begin{array}{l}\require{cancel}
2x=-7
\\\\
\dfrac{2x}{2}=-\dfrac{7}{2}
\\\\
x=-\dfrac{7}{2}
.\end{array}