#### Answer

$(-2,7)$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given inequality, $
-1\lt x+1 \lt 8
,$ use the properties of inequality.
For the interval notation, use a parenthesis for the symbols $\lt$ or $\gt.$ Use a bracket for the symbols $\le$ or $\ge.$
For graphing inequalities, use a hollowed dot for the symbols $\lt$ or $\gt.$ Use a solid dot for the symbols $\le$ or $\ge.$
$\bf{\text{Solution Details:}}$
Using the properties of inequality, the inequality above is equivalent to
\begin{array}{l}\require{cancel}
-1-1\lt x+1-1 \lt 8-1
\\\\
-2\lt x \lt 7
.\end{array}
In interval notation, the solution set is $
(-2,7)
.$
The red graph is the graph of the solution set.