Question

Сумма целых значений x, для которых верно неравенство 1/5 < 1/x < 1/2, равна... С оъяснением, спасибо!!!

Answer 1

Итак это мы можем разложить на 2 системы:
0,2<1/x
1/x<0.5
решение 1 уравнения:
1/5<1/x
1/5-1/x<0
x-5/5x<0
5x(x-5)<0
x(x-5)<0
x=(0;5)
решение 2 уравнения:
1/x-1/2<0
2-x<2x<0
2x(x-2)<0
x(2-x)<0
x=(-бесконечность;0) и (2;+ бесконечность)
найдем пересечение:
х=(2;5)
теперь найдем сумму:
3+4=7
ответ:7

Answer 2

Finding the Sum of Whole Numbers that Satisfy the Inequality

To find the sum of whole numbers that satisfy the inequality 1/5 < 1/x < 1/2, we need to determine the range of values for x that satisfy the inequality and then find the sum of those values.

Let's break down the inequality and solve it step by step:

1. 1/5 < 1/x < 1/2

To simplify the inequality, we can take the reciprocal of each term:

2. 5 > x > 2

This means that x must be greater than 2 and less than 5.

Now, let's find the whole numbers within this range and calculate their sum.

The whole numbers that satisfy the inequality are 3 and 4. Therefore, the sum of these whole numbers is:

3 + 4 = 7

So, the sum of the whole numbers that satisfy the inequality 1/5 < 1/x < 1/2 is 7.

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