In order to graph this inequality, first let's define some ordered pairs:
[tex]\begin{gathered} x=3\colon \\ y\ge2\cdot|2|-2 \\ y\ge2 \\ \\ x=2\colon \\ y\ge2\cdot|1|-2 \\ y\ge0 \\ \\ x=1\colon \\ y\ge2\cdot|0|-2 \\ y\ge-2 \\ \\ x=0\colon \\ y\ge2\cdot|-1|-2 \\ y\ge0 \\ \\ x=-1\colon \\ y\ge2\cdot|-2|-2 \\ y\ge2 \end{gathered}[/tex]Now, graphing these points and filling the region above the lines, we have:
Looking at the options, the point that is inside this region is the point (1, 0), therefore the correct option is the third one.
