Question

5-2х/х-4 больше или ровно 0

Answer 1

$\frac{5-2x}{x-4} \geq 0$
ОДЗ:
x-4≠0
x≠4
$\frac{5-2x}{x-4} \geq 0$ ⇒  $(5-2x)(x-4) \geq 0$
1. 5-2x=0
5=2x
x=2,5
2. x-4=0
x=4
 
Ответ: x∈[2,5; 4)

Answer 2

To determine the values of x for which the expression (5 - 2x) / (x - 4) is greater than or equal to 0, we need to find the critical points and analyze the intervals.

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

Numerator: 5 - 2x = 0 2x = 5 x = 5/2

Denominator: x - 4 = 0 x = 4

So, we have two critical points: x = 5/2 and x = 4.

Now, let's analyze the intervals created by these critical points.

Interval 1: (-∞, 4) Choose a test point in this interval, let's say x = 0. Plug the value into the expression: (5 - 2(0)) / (0 - 4) = 5/(-4) = -5/4 Since -5/4 is less than 0, the expression is negative in this interval.

Interval 2: (4, 5/2) Choose a test point in this interval, let's say x = 1. Plug the value into the expression: (5 - 2(1)) / (1 - 4) = 3/(-3) = -1 Since -1 is less than 0, the expression is negative in this interval.

Interval 3: (5/2, ∞) Choose a test point in this interval, let's say x = 3. Plug the value into the expression: (5 - 2(3)) / (3 - 4) = (-1)/(-1) = 1 Since 1 is greater than 0, the expression is positive in this interval.

To summarize the results:

• The expression (5 - 2x) / (x - 4) is negative in the intervals (-∞, 4) and (4, 5/2).
• The expression is positive in the interval (5/2, ∞).

Therefore, the values of x for which the expression is greater than or equal to 0 are x ∈ [5/2, ∞).