Question

(5-х) (3х-6)(х+5)<=0​

Answer 1

Ответ:

5-x=0

3x-6=0

X+3=0

X=5

X=2

X=-3

Answer 2

Объяснение:

Надеюсь понятно объяснила.

Answer 3

To solve the inequality (5-х) (3х-6)(х+5) ≤ 0, we can use the concept of interval notation and analyze the signs of the factors.

First, let's consider the critical points where the factors change sign. These occur when each factor equals zero. So we have:

1. 5 - x = 0 => x = 5
2. 3x - 6 = 0 => 3x = 6 => x = 2
3. x + 5 = 0 => x = -5

We can use these critical points to divide the number line into four intervals: (-∞, -5), (-5, 2), (2, 5), and (5, +∞). Now, we need to determine the sign of the expression (5-х) (3х-6)(х+5) in each interval.

Interval (-∞, -5): Let's choose a test point in this interval, for example, x = -6: (5 - (-6)) * (3(-6) - 6) * (-6 + 5) = (11) * (-24) * (-1) = -264 < 0

Interval (-5, 2): Choosing x = 0: (5 - 0) * (3(0) - 6) * (0 + 5) = (5) * (-6) * (5) = -150 < 0

Interval (2, 5): Choosing x = 3: (5 - 3) * (3(3) - 6) * (3 + 5) = (2) * (3) * (8) = 48 > 0

Interval (5, +∞): Choosing x = 6: (5 - 6) * (3(6) - 6) * (6 + 5) = (-1) * (18) * (11) = -198 < 0

From the analysis above, we can conclude that the expression (5-х) (3х-6)(х+5) ≤ 0 when x belongs to the intervals (-∞, -5) and (5, +∞).

In interval notation, the solution to the inequality is:

(-∞, -5] ∪ (5, +∞)