To find the solution to the compound inequality, we need to solve each inequality separately first:
[tex]\begin{gathered} 2x+6\le2 \\ 2x\le2-6 \\ 2x\le-4 \\ x\le\frac{-4}{2} \\ x\le-2 \end{gathered}[/tex][tex]\begin{gathered} 2x-2\ge4 \\ 2x\ge4+2 \\ 2x\ge6 \\ x\ge\frac{6}{2} \\ x\ge3 \end{gathered}[/tex]
The solution to the compound inequality is x<=-2 or x>=3.
