ExplanationThe 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: \(\frac{2+3+5}{3}=10/3\).
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