Answer
$(-\infty,-\frac{1}{3}]U[5,\infty)$.
Work Step by Step
Step 1. Factor the inequality, we have $3x^2-14x-5\ge0 \longrightarrow (x-5)(3x+1)\ge0$.
Step 2. Identify the boundary points $x=-\frac{1}{3}, 5$ and the intervals with these points $(-\infty,-\frac{1}{3}],[-\frac{1}{3},5],[5,\infty)$.
Step 3. Choose test values for each interval and test the inequality, $x=-1,0,6$, and the results are $True,\ False,\ True$.
Step 4. Thus, the solution intervals are $(-\infty,-\frac{1}{3}]U[5,\infty)$.
