Question

При каких значениях X функция у= 7-2х /3 принимает значение больше 0

Answer 1

7-2х/3>0
-2х/3>-7
2х/3<7
2х<21
х<10,5

Answer 2

Если x меньше или равен 3

Answer 3

To find the values of X for which the function y = (7 - 2x) / 3 takes on a value greater than 0, we need to solve the inequality y > 0.

The function is y = (7 - 2x) / 3.

1. Set y > 0: (7 - 2x) / 3 > 0

2. To solve the inequality, we can start by finding the critical points where the function is equal to 0 or undefined. The critical points occur when the numerator (7 - 2x) equals 0, which is when: 7 - 2x = 0 2x = 7 x = 7/2 x = 3.5

3. Now, let's set up a number line and test the intervals between the critical points and beyond:

   |----|------|----|--------|----| -∞ 3.5 4 5 6 +∞

4. Pick test points in each interval:

   • Test point in the interval (-∞, 3.5): x = 0
   • Test point in the interval (3.5, 4): x = 3.6
   • Test point in the interval (4, 5): x = 4.5
   • Test point in the interval (5, 6): x = 5.5
   • Test point in the interval (6, +∞): x = 7

5. Substitute the test points into the inequality and check the sign:

   • For x = 0: (7 - 2*0) / 3 = 7 / 3 > 0 (True)
   • For x = 3.6: (7 - 2*3.6) / 3 = -1.2 / 3 < 0 (False)
   • For x = 4.5: (7 - 2*4.5) / 3 = -2 / 3 < 0 (False)
   • For x = 5.5: (7 - 2*5.5) / 3 = -1 / 3 < 0 (False)
   • For x = 7: (7 - 2*7) / 3 = -7 / 3 < 0 (False)

6. Based on the above, we can conclude that the function y = (7 - 2x) / 3 is greater than 0 in the interval (-∞, 3.5), which means the valid range of x that makes the function greater than 0 is: x ∈ (-∞, 3.5)