Question

X+2/ 2-x больше или равно 0

Answer 1

Домножаем га -1 меняем знак, смотрим, где положительные значения и где отрицательные, пишем ответ.

Answer 2

To solve the inequality $\frac{x+2}{2-x} \geq 0$, we need to find the values of $x$ that satisfy the inequality.

Step 1: Find the critical points where the expression becomes undefined (denominator equals zero). $2-x = 0 \Rightarrow x = 2$

Step 2: Determine the sign of the expression in the intervals created by the critical points and points where the expression changes sign.

We have three intervals to consider:

1. $x < 2$
2. $x = 2$ (not included due to the division by zero)
3. $x > 2$

Step 3: Test a value in each interval to find the sign of the expression.

Let's pick $x = 0$ for $x < 2$: $\frac{0 + 2}{2 - 0} = \frac{2}{2} = 1$

Now, let's pick $x = 3$ for $x > 2$: $\frac{3 + 2}{2 - 3} = \frac{5}{-1} = -5$

Step 4: Determine where the expression is greater than or equal to zero.

1. $x < 2$ : $\frac{x+2}{2-x} = 1$ (positive)
2. $x > 2$ : $\frac{x+2}{2-x} = -5$ (negative)

The inequality $\frac{x+2}{2-x} \geq 0$ is satisfied for $x < 2$ and $x = 2$ (but not included). Thus, the solution to the inequality is: $x \in (-\infty, 2) \cup (2, +\infty)$