(X+13)(x-7)2(x-15)>0

Предыдущий
вопрос Следующий
вопрос

To solve this inequality, we first need to find the critical points by setting each factor equal to zero:

x + 13 = 0
x = -13

x - 7 = 0
x = 7

x - 15 = 0
x = 15

The critical points are x = -13, 7, and 15. We will use these critical points to create intervals on the number line and test each interval to determine which intervals satisfy the inequality.

Using the critical points, we have the intervals:
(-∞, -13), (-13, 7), (7, 15), (15, ∞)

We will test a value in each interval to see where the inequality is satisfied:
For x = -14 (-∞, -13):
(-1)(-21)(-29) > 0
This interval satisfies the inequality.

For x = 0 (-13, 7):
(13)(-7)(-15) < 0
This interval does not satisfy the inequality.

For x = 8 (7, 15):
(21)(1)(-7) > 0
This interval satisfies the inequality.

For x = 16 (15, ∞):
(29)(9)(1) > 0
This interval satisfies the inequality.

Therefore, the solution to the inequality (x+13)(x-7)(x-15) > 0 is (-∞, -13) U (7, 15) U (15, ∞).