Answer
no solution
Work Step by Step
Using the properties of equality, the given expression, $
\left| \dfrac{4(x-1)}{7} \right|+10\lt2
,$ is equivalent to
\begin{array}{l}\require{cancel}
\left| \dfrac{4(x-1)}{7} \right|\lt2-10
\\\\
\left| \dfrac{4(x-1)}{7} \right|\lt-8
.\end{array}
The left side of the expression, $
\left| \dfrac{4(x-1)}{7} \right|\lt-8
,$ always gives a non-negative value. This will never be less than or equal to the negative value at the right. Hence, there is no solution.