Question

x решите неравенство

Answer 1

Зададим функцию у=

D(y): x#1

Нули функции x=0,  x=-2

   -      +     -      +

____.____.____.____

     -2     0      1

xє(- бесконечность; -2)U(0; 1)

Answer 2

$\frac{x(x+2)}{x-1}<0$

Используя метод интервалов, получаем $x<-2,\ 0<x<1.$

Ответ: $x<-2,\ \ 0<x<1.$

Answer 3

Solving the Inequality

To solve the inequality (14 - 7x)(x + 3) > 0, we can follow these steps:

1. Find the critical points by setting each factor equal to zero and solving for x: - (14 - 7x) = 0 - x + 3 = 0

Solving these equations, we find: - x = 2 - x = -3

2. Create intervals based on the critical points: - Interval 1: (-∞, -3) - Interval 2: (-3, 2) - Interval 3: (2, +∞)

3. Test a value from each interval in the original inequality to determine the sign of the expression: - For Interval 1, let's test x = -5: - (14 - 7(-5))(-5 + 3) = (14 + 35)(-2) = -98 < 0 - The expression is negative in Interval 1.

- For Interval 2, let's test x = 0: - (14 - 7(0))(0 + 3) = 14 * 3 = 42 > 0 - The expression is positive in Interval 2.

- For Interval 3, let's test x = 5: - (14 - 7(5))(5 + 3) = (14 - 35)(8) = -168 < 0 - The expression is negative in Interval 3.

4. Determine the solution based on the signs of the expression in each interval: - The inequality is satisfied when the expression is greater than zero. - Therefore, the solution is: - x ∈ (-∞, -3) U (2, +∞)

So, the solution to the inequality (14 - 7x)(x + 3) > 0 is x ∈ (-∞, -3) U (2, +∞).