Answer
$x=\left\{ -\dfrac{3}{2},\dfrac{1}{2} \right\}$
Work Step by Step
Using the properties of equality, the given equation, $
|4x+2|-7=-3
,$ is equivalent to
\begin{array}{l}\require{cancel}
|4x+2|=-3+7
\\\\
|4x+2|=4
.\end{array}
Since for any $a\gt0$, $|x|=a$ implies $x=a$ or $x=-a$, then the equation above is equivalent to
\begin{array}{l}\require{cancel}
4x+2=4 \text{ OR } 4x+2=-4
.\end{array}
Solving each equation results to
\begin{array}{l}\require{cancel}
4x+2=4
\\\\
4x=4-2
\\\\
4x=2
\\\\
x=\dfrac{2}{4}
\\\\
x=\dfrac{1}{2}
\\\\\text{ OR }\\\\
4x+2=-4
\\\\
4x=-4-2
\\\\
4x=-6
\\\\
x=-\dfrac{6}{4}
\\\\
x=-\dfrac{3}{2}
.\end{array}
Hence, the solutions are $
x=\left\{ -\dfrac{3}{2},\dfrac{1}{2} \right\}
.$
