Question

(x-5,7)(x-7,2)>0; (x-2,5)(3-x)<0. решите пожалуйста=)

Answer 1

(x-5,7)(x-7,2))>0   x>5,7; х>7,2

(x-2,5)(3-x)<0    х<2,5; х>3

Answer 2

Solving the Inequalities

To solve the inequalities (x-5.7)(x-7.2) > 0 and (x-2.5)(3-x) < 0, we can use a method called the sign chart or interval notation. This method involves finding the critical points and testing intervals to determine the sign of the expression within each interval.

Let's solve each inequality separately:

# (x-5.7)(x-7.2) > 0

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

1. Find the critical points by setting the expression equal to zero and solving for x: - (x-5.7)(x-7.2) = 0 - x = 5.7 or x = 7.2

2. Create a sign chart by selecting test points in each interval: - Choose a test point less than 5.7, such as x = 0. - Choose a test point between 5.7 and 7.2, such as x = 6. - Choose a test point greater than 7.2, such as x = 10.

3. Evaluate the expression at each test point: - For x = 0: (0-

Answer 3

Solving the Inequalities

To solve the inequalities (x-5.7)(x-7.2) > 0 and (x-2.5)(3-x) < 0, we can use the method of sign charts.

Let's solve each inequality separately:

1. (x-5.7)(x-7.2) > 0:

To determine the sign of the expression (x-5.7)(x-7.2), we need to find the critical points where the expression equals zero. In this case, the critical points are x = 5.7 and x = 7.2.

We can create a sign chart to analyze the sign of the expression in different intervals:

| Interval | (x-5.7)(x-7.2) | |----------|----------------| | x < 5.7 | (+) | | 5.7 < x < 7.2 | (-) | | x > 7.2 | (+) |

From the sign chart, we can see that the expression is positive when x < 5.7 and x > 7.2, and negative when 5.7 < x < 7.2.

Therefore, the solution to the inequality (x-5.7)(x-7.2) > 0 is x < 5.7 or x > 7.2.

2. (x-2.5)(3-x) < 0:

Similarly, let's find the critical points where the expression (x-2.5)(3-x) equals zero. In this case, the critical points are x = 2.5 and x = 3.

Using a sign chart, we can analyze the sign of the expression in different intervals:

| Interval | (x-2.5)(3-x) | |----------|--------------| | x < 2.5 | (-) | | 2.5 < x < 3 | (+) | | x > 3 | (-) |

From the sign chart, we can see that the expression is negative when x < 2.5 and x > 3, and positive when 2.5 < x < 3.

Therefore, the solution to the inequality (x-2.5)(3-x) < 0 is 2.5 < x < 3.

Summary of Solutions

To summarize, the solutions to the given inequalities are:

1. (x-5.7)(x-7.2) > 0: x < 5.7 or x > 7.2. 2. (x-2.5)(3-x) < 0: 2.5 < x < 3.

Please note that these solutions are based on the given inequalities and the method of sign charts.