Chapter 2: Q10. (page 107)

If n is a prime integer such that $2 n > 19 \geq \frac{7}{8} n$ what is one possible value of n?

Short Answer

Expert verified

The one possible value forn is 11.

Step by step solution

Step-1 – Apply the concept of prime integers

The set of integers are the positive and negative whole numbers including 0 and is expressed as $\dots, - 2, - 1, 0, 1, 2, \dots$ .

The set of prime numbers are those numbers which have only two factors that are 1 and number itself.

Step-2 –Solve the inequality

Consider the provided inequality $2 n > 19 \geq \frac{7}{8} n$ .

Divide the inequality by n.

$\begin{matrix} \frac{2 n}{n} > \frac{19}{n} \geq \frac{7}{8} \frac{n}{n} \\ 2 > \frac{19}{n} \geq \frac{7}{8} \end{matrix}$

Take the reciprocal and reverse the order of inequality.

$\begin{matrix} \frac{2 n}{n} > \frac{19}{n} \geq \frac{7}{8} \frac{n}{n} \\ 2 > \frac{19}{n} \geq \frac{7}{8} \\ \frac{1}{2} < \frac{n}{19} \leq \frac{8}{7} \end{matrix}$

Step-3 –Simplify the inequality

Multiply the inequality by 19.

$\begin{matrix} \frac{1}{2} \cdot 19 < \frac{n}{19} \cdot 19 \leq \frac{8}{7} \cdot 19 \\ \frac{19}{2} < n \leq \frac{152}{7} \end{matrix}$

Convert to decimal notation.

$9.5 < n \leq 21.71$

Now, the prime integers that lie between 9.5 and 21.71 are possible values of n.

Therefore, one prime integer is 11. Because only factors of 11 are 1 and 11 only.

Thus, the one possible value for n is 11.

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If n is a prime integer such that $2 n > 19 \geq \frac{7}{8} n$ what is one possible value of n?

Short Answer

Step by step solution

Step-1 – Apply the concept of prime integers

Step-2 –Solve the inequality

Step-3 –Simplify the inequality

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If n is a prime integer such that2n>19≥78nwhat is one possible value of n?

Short Answer

Step by step solution

Step-1 – Apply the concept of prime integers

Step-2 –Solve the inequality

Step-3 –Simplify the inequality

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

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Theoretical and Mathematical Physics

Applied Mathematics

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Logic and Functions

Study anywhere. Anytime. Across all devices.

If n is a prime integer such that $2 n > 19 \geq \frac{7}{8} n$ what is one possible value of n?