#### Answer

$[-6, -0.5] ∪ [1, ∞)$

#### Work Step by Step

Given: The inequality $2x^{3}+11x^{2}≥7x+6$
Rewrite the polynomial Inequality as follows:
$2x^{3}+11x^{2}-7x-6≥0$
According to the graph given in the question, the intervals of f(x) greater than 0 are$[-6, -0.5]$ or $[1, ∞)$.
Thus, the interval notation of the inequality is$[-6, -0.5] ∪ [1, ∞)$ .