Answer
$x=4$
Work Step by Step
The given inequality, $
7x-1\le7+5x\le3(1+2x)
,$ is equivalent to
\begin{array}{l}\require{cancel}
7x-1\le7+5x
\text{ and }
7+5x\le3(1+2x)
.\end{array}
Solving the inequalities separately results to
\begin{array}{l}\require{cancel}
7x-1\le7+5x
\\
7x-5x\le7+1
\\
2x\le8
\\
x\le\dfrac{8}{2}
\\
x\le4
\\\\\text{ and } \\\\
7+5x\le3(1+2x)
\\
7+5x\le3+6x
\\
5x-6x\le3-7
\\
-x\le-4
\\
x\ge\dfrac{-4}{-1}
\\
x\ge4
.\end{array}
Since "and" is used, then the solution set is the intersection of the two inequalities. Hence, the solution set is $
x=4
.$