Let's solve the inequality first:
[tex]\begin{gathered} \frac{1}{2}x+2\ge1 \\ x+4\ge2 \\ x\ge-2 \\ or \\ \frac{1}{2}x+2\leq-1 \\ x+4\leq-2 \\ x\leq-6 \end{gathered}[/tex][tex]\begin{gathered} 4x+2<10 \\ 4x<8 \\ x<2 \\ or \\ 4x+2>-10 \\ 4x>-12 \\ x>-3 \\ -3