#### Answer

no solution

#### Work Step by Step

The given inequality, $
|3-4x|+7\lt-4
,$ is equivalent to
\begin{array}{l}\require{cancel}
|3-4x|\lt-4-7
\\\\
|3-4x|\lt-11
.\end{array}
For any $x$, the left side of the inequality above is always a non negative number. This is never less than the negative number at the right. Hence, there is $\text{
no solution
.}$