ANSWER
[5, ∞)
EXPLANATION
First we have to solve each inequality separately:
[tex]\begin{gathered} x+1\ge2 \\ x\ge2-1 \\ x\ge1 \end{gathered}[/tex]
And the other inequality
[tex]\begin{gathered} 2x-8\ge2 \\ 2x\ge2+8 \\ 2x\ge10 \\ x\ge\frac{10}{2} \\ x\ge5 \end{gathered}[/tex]
Graphing this solution set:
Solution x ≥ 5 includes solution x ≥ 1, so the solution is [5, ∞)
