#### Answer

$\left[ 1,7 \right]$

#### Work Step by Step

Using the properties of inequality, the given inequality, $
-1\le6-x\le5
,$ simplifies to
\begin{array}{l}\require{cancel}
-1-6\le6-6-x\le5-6
\\\\
-7\le-x\le-1
\\\\
7\ge x\ge1
\\\\
1\le x\le7
.\end{array}
Hence, the solution is the interval $
\left[ 1,7 \right]
.$