Question

Знайдіть усі натуральні значення х ,при яких є правильною нерівність: 1) 3 11/15 < х/15 < 4 2) 3 1/8 < 25/х < 8 1/3Помогите пожалуйста, с объяснением!!​

Answer 1

1) 3 11/15=3*15+11=56/15

   4 = 3 15/15

  56/15<x/15<3 15/15

   x=57; 58; 59

2) 3 1/8<25/x<8 1/3

   3 1/8=25/8

   8 1/3=25/3

   25/8<25/x<25/3

   x=4; 5; 6; 7

Answer 2

Finding Natural Values of x for the Given Inequalities

To find all the natural values of x for which the inequalities are true, we'll solve each inequality separately.

Inequality 1: 3 11/15 < x/15 < 4

To solve the first inequality, we can multiply each part of the inequality by 15 to clear the fraction:

Step 1: Multiply each part by 15: - 3 11/15 * 15 < x < 4 * 15 - 56 < x < 60

So, the natural values of x for the first inequality are all the natural numbers between 56 and 60, inclusive.

Inequality 2: 3 1/8 < 25/x < 8 1/3

To solve the second inequality, we'll first find the reciprocal of each part of the inequality and then multiply each part by 25:

Step 1: Find the reciprocal of each part: - 1 / (8 1/3) < 25/x < 1 / (3 1/8) - 3/25 < 25/x < 8/1

Step 2: Multiply each part by 25: - 3 < x < 200

So, the natural values of x for the second inequality are all the natural numbers between 3 and 200, inclusive.

Conclusion

The natural values of x that satisfy the given inequalities are all the natural numbers between 56 and 60 (inclusive) for the first inequality, and all the natural numbers between 3 and 200 (inclusive) for the second inequality.