Question

(x+8)(x-5)(x+10)<0 решите плз??

Answer 1

(x+8)(x-5)(x+10)<0
нули : -10, -8,  5
       -                +                      -                            +
--------------I-----------I-----------------------I-----------------------------
              -10          -8                           5
x∈(-∞;-10)U(-8;5)

Answer 2

To solve the inequality (x+8)(x-5)(x+10) < 0, we can use the concept of interval notation and the sign chart method.

Sign Chart Method:

1. Find the critical points by setting each factor equal to zero and solving for x: - x + 8 = 0 => x = -8 - x - 5 = 0 => x = 5 - x + 10 = 0 => x = -10

2. Plot the critical points on a number line and divide it into four intervals: - Interval 1: (-∞, -10) - Interval 2: (-10, -8) - Interval 3: (-8, 5) - Interval 4: (5, +∞)

3. Choose a test point from each interval and evaluate the sign of the expression (x+8)(x-5)(x+10): - Test point for Interval 1: x = -11 - (-11+8)(-11-5)(-11+10) = (-3)(-16)(-1) = -48 - The expression is negative in Interval 1.

- Test point for Interval 2: x = -9 - (-9+8)(-9-5)(-9+10) = (-1)(-14)(1) = 14 - The expression is positive in Interval 2.

- Test point for Interval 3: x = 0 - (0+8)(0-5)(0+10) = (8)(-5)(10) = -400 - The expression is negative in Interval 3.

- Test point for Interval 4: x = 6 - (6+8)(6-5)(6+10) = (14)(1)(16) = 224 - The expression is positive in Interval 4.

4. Determine the solution by analyzing the signs: - The expression is negative in Interval 1 and Interval 3. - Therefore, the solution to the inequality (x+8)(x-5)(x+10) < 0 is x ∈ (-∞, -10) ∪ (5, +∞).

Solution:

The solution to the inequality (x+8)(x-5)(x+10) < 0 is x ∈ (-∞, -10) ∪ (5, +∞).