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If x equals all prime numbers that satisfy the inequality
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09 Dec 2017, 18:29
09 Dec 2017, 18:29
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Question Stats:
57% (02:00) correct
42% (02:43) wrong based on 83 sessions
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If x equals all prime numbers that satisfy the inequality \(|\frac{1}{10-x}|\leq \frac{5}{x^2}\) what is the average value of x ?
Drill 3
Question: 6
Page: 529
Question: 6
Page: 529
Show: :: OA
\(\frac{10}{3}\)
Re: If x equals all prime numbers that satisfy the inequality
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29 Dec 2017, 14:27
29 Dec 2017, 14:27
5
Expert Reply
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: \(\frac{2+3+5}{3}=10/3\).
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: \(\frac{2+3+5}{3}=10/3\).
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Re: If x equals all prime numbers that satisfy the inequality
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17 Jun 2019, 05:15
17 Jun 2019, 05:15
6
akshata96 wrote:
-2,-3 and -5 are also prime numbers and satisfy the equation as they have not specified only positive integers why not take the negative as well?
A prime number is defined as "an integer greater than 1 that has only two positive divisors: 1 and itself"
Cheers,
Brent
