Question

-2/x>10 решите неравенство

Answer 1

Ответ:

(-2-10х)/х больше 0 ;

Объяснение:

-2(1+5х)/х больше 0; разделим на (-2), знак неравенства измениттся на противоположный .

(1+5х)/х меньше 0. найдем корни: х=о, х=(-0,2), значит х€(-0,2 ;0).

Answer 2

To solve the inequality $-\frac{2}{x} > 10$, follow these steps:

Step 1: Remove the fraction by multiplying both sides of the inequality by $x$. However, since we are multiplying by $x$, we need to consider two cases:

Case 1: $x > 0$ If $x > 0$, we can multiply both sides of the inequality by $x$ without changing the direction of the inequality.

$-2 > 10x$

Step 2: Isolate $x$ on one side of the inequality. To do this, subtract $10x$ from both sides:

$-2 - 10x > 0$

Step 3: Simplify the inequality:

$-10x - 2 > 0$

Step 4: Now, solve for $x$:

Add 2 to both sides:

$-10x > 2$

Step 5: Finally, divide both sides by -10. Remember, since we are dividing by a negative number, the direction of the inequality will flip.

$x < -\frac{2}{10}$

$x < -\frac{1}{5}$

Case 2: $x < 0$ If $x < 0$, we need to multiply both sides of the inequality by $x$ and, therefore, reverse the direction of the inequality:

$-2 < 10x$

Step 2: Isolate $x$ on one side of the inequality by subtracting $10x$ from both sides:

$-2 - 10x < 0$

Step 3: Simplify the inequality:

$-10x - 2 < 0$

Step 4: Now, solve for $x$:

Add 2 to both sides:

$-10x < 2$

Step 5: Finally, divide both sides by -10. Remember, since we are dividing by a negative number, the direction of the inequality will flip again:

$x > \frac{2}{10}$

$x > \frac{1}{5}$

Now we have two solutions:

1. If $x > 0$, then $x < -\frac{1}{5}$
2. If $x < 0$, then $x > \frac{1}{5}$

Thus, the solution to the inequality $-\frac{2}{x} > 10$ is $x < -\frac{1}{5}$ or $x > \frac{1}{5}$.