Answer
no solution
Work Step by Step
The given inequality, $
|10x+7|+3\lt1
,$ is equivalent to
\begin{array}{l}\require{cancel}
|10x+7|\lt1-3
\\\\
|10x+7|\lt-2
.\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 $\text{
no solution
.}$