Question

(x + 1)(x - 4)(3x - 6) < 0 Срчн

Answer 1

Возможно, так..........

Answer 2

To find the solution to the inequality (x + 1)(x - 4)(3x - 6) < 0, we can analyze the signs of the expressions involved and determine the intervals where the inequality is satisfied.

Let's break it down step by step:

1. Find the critical points: To determine the critical points, we set each factor equal to zero and solve for x:

x + 1 = 0 -> x = -1 x - 4 = 0 -> x = 4 3x - 6 = 0 -> x = 2

So, the critical points are x = -1, x = 2, and x = 4.

2. Create sign intervals: We'll divide the number line into four intervals based on the critical points:

Interval 1: (-∞, -1) Interval 2: (-1, 2) Interval 3: (2, 4) Interval 4: (4, +∞)

3. Determine the sign of each factor in each interval: Now, we'll determine the sign of each factor in each interval.

Interval 1: (-∞, -1) In this interval, we can choose x = -2 (a value less than -1) to evaluate the signs: (x + 1) = (-2 + 1) = -1 (negative) (x - 4) = (-2 - 4) = -6 (negative) (3x - 6) = (3(-2) - 6) = -12 (negative)

Interval 2: (-1, 2) In this interval, we can choose x = 0 (a value between -1 and 2) to evaluate the signs: (x + 1) = (0 + 1) = 1 (positive) (x - 4) = (0 - 4) = -4 (negative) (3x - 6) = (3(0) - 6) = -6 (negative)

Interval 3: (2, 4) In this interval, we can choose x = 3 (a value between 2 and 4) to evaluate the signs: (x + 1) = (3 + 1) = 4 (positive) (x - 4) = (3 - 4) = -1 (negative) (3x - 6) = (3(3) - 6) = 3 (positive)

Interval 4: (4, +∞) In this interval, we can choose x = 5 (a value greater than 4) to evaluate the signs: (x + 1) = (5 + 1) = 6 (positive) (x - 4) = (5 - 4) = 1 (positive) (3x - 6) = (3(5) - 6) = 9 (positive)

4. Determine the sign of the whole expression: To determine the sign of the whole expression (x + 1)(x - 4)(3x - 6), we look at the signs of each factor in each interval:

Interval 1: (-∞, -1)

• • • = - (negative)

Interval 2: (-1, 2)

• • • = + (positive)

Interval 3: (2, 4)

• • • = - (negative)

Interval 4: (4, +∞)

• • • = + (positive)

5. Identify the solution: From the sign analysis, we can see that the expression (x + 1)(x - 4)(3x