2 < x/15 < 4/5 tengsizlikni qanoatlantiruvchi nechta natural x soni mavjud?

We are looking for the number of natural numbers 'x' that satisfy the inequality:

\( \frac{2}{5} < \frac{x}{15} < \frac{4}{5} \)

To solve this, we can multiply all parts of the inequality by 15 to isolate 'x':

\[ 15 \cdot \frac{2}{5} < 15 \cdot \frac{x}{15} < 15 \cdot \frac{4}{5} \]

Now, we simplify:

\[ 3 \cdot 2 < x < 3 \cdot 4 \]

\[ 6 < x < 12 \]

The natural numbers 'x' that are strictly greater than 6 and strictly less than 12 are 7, 8, 9, 10, and 11.

There are 5 such natural numbers.

Ответ: 5