#### Answer

$\left( -6,8 \right)$

#### Work Step by Step

Since for any $a\gt0$, $|x|\lt a$ implies $-a\lt x\lt a,$ then the given inequality, $
|x-1|\lt7
,$ is equivalent to
\begin{array}{l}\require{cancel}
-7\lt x-1\lt7
.\end{array}
Using the properties of inequality, then
\begin{array}{l}\require{cancel}
-7+1\lt x-1+1\lt7+1
\\\\
-6\lt x\lt8
.\end{array}
Hence, the solution is the interval $
\left( -6,8 \right)
.$