List the critical values of the related function. Then solve the inequality. \[ \frac{x+5}{x-10} \geq 3 \] The critical value(s) is/are $\frac{35}{2}, 10$. (Simplify your answer. Type an integer or a simplified fraction. Type an exact answer, using radi The solution set is (Simplify your answer. Type your answer in interval notation. Use integers or fractions for any n as needed.)

Step 1 ：First, identify the critical values of the function. The critical values are the values of x that make the function undefined or the values of x that make the numerator zero. In this case, the function is undefined when x = 10 and the numerator is zero when x = -5. However, the question already provides the critical values as \(\frac{35}{2}\) and 10.

Step 2 ：Solve the inequality \(\frac{x+5}{x-10} \geq 3\) to find the values of x that satisfy it. The solution to the inequality is x = \(\frac{35}{2}\).

Step 3 ：Consider the critical values and the intervals they create. The critical values divide the number line into three intervals: (-∞, 10), (10, \(\frac{35}{2}\)), and (\(\frac{35}{2}\), ∞). Test a number from each interval in the inequality to determine which intervals are part of the solution set.

Step 4 ：The test results show that the inequality is satisfied in the interval (10, \(\frac{35}{2}\)). Therefore, the solution set to the inequality is (10, \(\frac{35}{2}\)).

Step 5 ：Final Answer: The solution set to the inequality is \(\boxed{(10, \frac{35}{2})}\).