Answer
$x\in \left[ 1,3 \right]$
Work Step by Step
We have to solve the given inequality for x:
$\begin{align}
& \left| 2x-4 \right|\le 2 \\
& \text{or,}\,\,-2\le (2x-4)\le 2\,\,\,\,\,\,\,\,\left[ \text{Recall that, for}\,\,\left| a \right|\le b\,\,\text{implies}\,\,-b\le a\le b \right] \\
& \text{or,}\,\,2\le 2x\le 6\,\,\,\,\,\,\, \\
& \text{or,}\,\,1\le x\le 3\,
\end{align}$
