Answer
$\left[ 2,\infty \right)$
Work Step by Step
Solving the inequalities separately, then,
\begin{array}{l}
x+2\ge3\\
x\ge1
,\\\\\text{and}\\\\
5x-1\ge9\\
5x\ge10\\
x\ge2
.\end{array}
Using the conjunction "and", then the solution set is the set common to both inequalities. Hence, the solution set is $
\left[ 2,\infty \right)
$.
