Answer
$(-\infty,-5]\cup[2,\infty)$.
Work Step by Step
Step 1. For $x^2+3x-10\ge0 \Longrightarrow (x-2)(x+5)\ge0$, identify boundary points as $x=-5,2$.
Step 2. Form intervals $(-\infty,-5],[-5,2],[2,\infty)$.
Step 3. Choose test values for each interval $x=-6,0,3$.
Step 4. Test the inequality to get results: $True,\ False,\ True$
Step 5. We have the solution $(-\infty,-5]\cup[2,\infty)$.
