Explanation

The most efficient way to approach this tough problem is to plug in prime numbers to determine the set of values that satisfies the inequality. Plugging 2 in for x yields $\frac{1}{8} \leq \frac{5}{4}$ which is true.

Plugging in 3 yields $\frac{1}{7} \leq \frac{5}{9}$ which is also true.

Plugging in 5 yields $\frac{1}{5} \leq \frac{5}{25}$ so the two sides are equal, so that’s probably the maximum value of x.

To be sure, check the next prime number, 7: $\frac{1}{7} \leq \frac{5}{49}$ which is false.

You should also check a large prime number to confirm {2, 3, 5} is the solution set. If you do, you’ll find the inequality is false and {2, 3, 5} is the full set of values. To find the average of the numbers, use the Average Pie: $\frac{2+3+5}{3}=10/3$.