Question

13 + х --------- > 0 2,5 х 2 х - 4 --------- >0 х + 2

Answer 1

Ответ смотри на фото.

Answer 2

To solve the inequalities, we need to find the values of x that make each expression greater than zero.

1. $\frac{13 + x}{2.5x} > 0$:

To solve this inequality, we need to consider three intervals based on the sign of $x$.

Interval 1: $x < -2$: Let's pick $x = -3$ (any value smaller than -2 will work). Then the expression becomes: $\frac{13 - 3}{2.5(-3)} = \frac{10}{-7.5} = -\frac{4}{3}$. Since this value is negative, this interval does not satisfy the inequality.

Interval 2: $-2 < x < -\frac{2}{3}$: Let's pick $x = -1$ (any value between -2 and -\frac{2}{3} will work). Then the expression becomes: $\frac{13 - 1}{2.5(-1)} = \frac{12}{-2.5} = -\frac{24}{5}$. Since this value is negative, this interval does not satisfy the inequality.

Interval 3: $x > -\frac{2}{3}$: Let's pick $x = 1$ (any value greater than -\frac{2}{3} will work). Then the expression becomes: $\frac{13 + 1}{2.5(1)} = \frac{14}{2.5} = \frac{28}{5}$. Since this value is positive, this interval satisfies the inequality.

So, the solution to the inequality $\frac{13 + x}{2.5x} > 0$ is $x > -\frac{2}{3}$.

2. $\frac{2x - 4}{x + 2} > 0$:

To solve this inequality, we need to consider two intervals based on the sign of $x$.

Interval 1: $x < -2$: Let's pick $x = -3$ (any value smaller than -2 will work). Then the expression becomes: $\frac{2(-3) - 4}{-3 + 2} = \frac{-10}{-1} = 10$. Since this value is positive, this interval satisfies the inequality.

Interval 2: $x > -2$: Let's pick $x = 1$ (any value greater than -2 will work). Then the expression becomes: $\frac{2(1) - 4}{1 + 2} = \frac{-2}{3}$. Since this value is negative, this interval does not satisfy the inequality.

So, the solution to the inequality $\frac{2x - 4}{x + 2} > 0$ is $x < -2$.

In summary, the solutions to the given inequalities are:

1. $x > -\frac{2}{3}$
2. $x < -2$