#### Answer

The solutions are $x=-1$ and $x=-\dfrac{1}{2}$

#### Work Step by Step

$|4x+3|-2=-1$
Take $2$ to the right side:
$|4x+3|=-1+2$
$|4x+3|=1$
Solving this absolute value equation is equivalent to solving two separate equations, which are:
$4x+3=1$ and $4x+3=-1$
$\textbf{Solve the first equation:}$
$4x+3=1$
Take $3$ to the right side:
$4x=1-3$
$4x=-2$
Solve for $x$:
$x=-\dfrac{2}{4}$
$x=-\dfrac{1}{2}$
$\textbf{Solve the second equation:}$
$4x+3=-1$
Take $3$ to the right side:
$4x=-1-3$
$4x=-4$
Solve for $x$:
$x=-\dfrac{4}{4}$
$x=-1$
The solutions are $x=-1$ and $x=-\dfrac{1}{2}$