Answer
$\left[ 2, \dfrac{5}{2} \right]$
Work Step by Step
Using compound inequalities, the solution to the given inequality, $
1\le4x-7\le3
,$ is
\begin{array}{l}\require{cancel}
1+7\le4x-7+7\le3+7
\\\\
8\le4x\le10
\\\\
\dfrac{8}{4}\le\dfrac{4}{4}x\le\dfrac{10}{4}
\\\\
2\le x\le\dfrac{5}{2}
.\end{array}
In interval notation, the solution is $
\left[ 2, \dfrac{5}{2} \right]
.$
