List the critical values of the related function. Then solve the inequality. \[ \frac{4 x}{x+6} \geq 0 \] The critical value(s) is/are $-6,0$. (Simplify your answer. Type an integer or a simplified fraction. Type an exact answer, using radica comma to separate answers as needed.) The solution set is (Simplify your answer. Type your answer in interval notation. Use integers or fractions for any numbers in the expr Type an exact answer, using radicals as needed.)

Step 1 ：Identify the critical values of the function. The critical values are the values of x that make the function equal to zero or undefined. In this case, the function is undefined when the denominator is zero, i.e., x = -6. The function is zero when the numerator is zero, i.e., x = 0. So, the critical values are -6 and 0.

Step 2 ：To solve the inequality, we need to consider the intervals defined by the critical values, which are (-∞, -6), (-6, 0), and (0, ∞). We need to test a value from each interval in the inequality to see if it is true. If it is true, then the entire interval is part of the solution set.

Step 3 ：Test the values -7, -1, and 1 in the inequality. The test values -7 and 1 make the inequality true, so the intervals (-∞, -6) and (0, ∞) are part of the solution set. The test value -1 does not make the inequality true, so the interval (-6, 0) is not part of the solution set.

Step 4 ：\(\boxed{(-\infty, -6) \cup (0, \infty)}\) is the solution set.