#### Answer

no solution

#### Work Step by Step

The given inequality, $
|4x+1|-2\lt-5
,$ is equivalent to
\begin{array}{l}\require{cancel}
|4x+1|\lt-5+2
\\\\
|4x+1|\lt-3
.\end{array}
For any $x$, the left side of the inequality above is a non-negative number. This is never less than the negative number at the right. Hence, there is $\text{
no solution
.}$