Answer
$\left( -\infty,\infty \right)$
Work Step by Step
Using the properties of inequality, the expression $
4(x-1)\ge4x-8
$ simplifies to
\begin{array}{l}
4x-4\ge4x-8\\
4x-4x\ge-8+4\\
0\ge-4 \text{ (TRUE)}
.\end{array}
Since the solution above ended with a TRUE statement, then the solution set is the set of all real numbers. In interval notation, the solution set is $
\left( -\infty,\infty \right)
$.