Question

При каких значениях х функция у = (7-2х) : 3 принимает положительные значения?​

Answer 1

Ответ:

Ответ: х<10,5

Пошаговое объяснение:

7-2х/3>0

-2х/3>-7

2х/3<7

2х<21

х<10,5

Answer 2

To find the values of x for which the function y = (7 - 2x) / 3 takes positive values, we need to solve the inequality y > 0:

(7 - 2x) / 3 > 0

First, let's find the critical points by setting the numerator equal to zero:

7 - 2x = 0 2x = 7 x = 7/2

Now, let's analyze the sign of the expression (7 - 2x) / 3 in three intervals: x < 7/2, x = 7/2, and x > 7/2.

1. For x < 7/2: Let's take x = 0 (a value less than 7/2): y = (7 - 2(0)) / 3 = 7 / 3, which is positive.

2. For x = 7/2: Let's take x = 7/2: y = (7 - 2(7/2)) / 3 = (7 - 7) / 3 = 0, which is not positive (but zero).

3. For x > 7/2: Let's take x = 4 (a value greater than 7/2): y = (7 - 2(4)) / 3 = (7 - 8) / 3 = -1 / 3, which is negative.

From the analysis above, we see that the function y = (7 - 2x) / 3 is positive when x is less than 7/2, i.e., the interval (−∞, 7/2). Therefore, the values of x for which the function takes positive values are all real numbers in the interval (−∞, 7/2).