Q10. If n is a prime integer such tha... [FREE SOLUTION]

Chapter 2: Q10. (page 107)

If n is a prime integer such that $2 n > 19 鈮� \frac{7}{8} n$ 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 $鈥�, 鈭� 2, 鈭� 1, 0, 1, 2, 鈥�$ .

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 $2 n > 19 鈮� \frac{7}{8} n$ .

Divide the inequality by n.

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

Take the reciprocal and reverse the order of inequality.

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

Step-3 –Simplify the inequality

Multiply the inequality by 19.

$\begin{matrix} \frac{1}{2} 鈰� 19 < \frac{n}{19} 鈰� 19 鈮� \frac{8}{7} 鈰� 19 \\ \frac{19}{2} < n 鈮� \frac{152}{7} \end{matrix}$

Convert to decimal notation.

$9.5 < n 鈮� 21.71$

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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91影视

If n is a prime integer such that $2 n > 19 鈮� \frac{7}{8} n$ 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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91影视

If n is a prime integer such that2n>19鈮�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

Pure Maths

Theoretical and Mathematical Physics

Discrete Mathematics

Decision Maths

Applied Mathematics

Logic and Functions

Study anywhere. Anytime. Across all devices.

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