#### Answer

$(1, 11)$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given inequality, $
-4\lt x-5\lt6
,$ 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}
-4+5\lt x-5+5\lt6+5
\\\\
1\lt x\lt11
.\end{array}
In interval notation, the solution set is $
(1, 11)
.$
The red graph is the graph of the solution set.