Answer
$x=\{ -11,8 \}$
Work Step by Step
Since for any $a\gt0$, $|x|=a$ implies $x=a$ OR $x=-a$, then the given equation, $
|2x+3|=19
,$ is equivalent to
\begin{array}{l}\require{cancel}
2x+3=19 \text{ OR } 2x+3=-19
.\end{array}
Solving each equation results to
\begin{array}{l}\require{cancel}
2x+3=19
\\\\
2x=19-3
\\\\
2x=16
\\\\
x=\dfrac{16}{2}
\\\\
x=8
\\\\\text{ OR }\\\\
2x+3=-19
\\\\
2x=-19-3
\\\\
2x=-22
\\\\
x=-\dfrac{22}{2}
\\\\
x=-11
.\end{array}
Hence, the solutions are $
x=\{ -11,8 \}
.$
