Question

Решение неравенства.Помогите пожалуйста решить неравенство и определить сколько целых решений оно имеет на промежутке [-6; 6]. Заранее большое спасибо!9*(2x-7) < 2корня из 22*(2х-7)*Неужели так сложно, что никто не поможет?(((

Answer 1

9*(2x-7) - 2корня из 22*(2х-7)<0
(2x-7)(9-2√22)<0
2x-7>0,т.к  9-2√22<0
2x>7
x>3,5
x∈(3,5;6]
x=4;5;6- 3 решения

Answer 2

Solving the Inequality

To solve the given inequality, we will follow these steps:

1. Simplify the expression on the left-hand side of the inequality. 2. Solve the resulting equation. 3. Determine the number of integer solutions within the given interval.

Let's apply these steps to the given inequality:

9*(2x-7) < 2√(22*(2x-7))

Step 1: Simplify the expression on the left-hand side of the inequality.

To simplify the expression, we can start by dividing both sides of the inequality by √(22*(2x-7)):

(9*(2x-7))/(√(22*(2x-7))) < 2

Simplifying further, we can cancel out the common factor of (2x-7):

9/√(22) < 2

Step 2: Solve the resulting equation.

To solve the equation, we need to isolate x. Let's square both sides of the equation to eliminate the square root:

(9/√(22))^2 < 2^2

Simplifying further:

81/22 < 4

Step 3: Determine the number of integer solutions within the given interval.

To find the number of integer solutions within the interval [-6, 6], we need to check if any integer values of x satisfy the inequality.

Let's evaluate the inequality for x = -6, -5, -4, ..., 6:

For x = -6: 81/22 < 4 (True) For x = -5: 81/22 < 4 (True) For x = -4: 81/22 < 4 (True) For x = -3: 81/22 < 4 (True) For x = -2: 81/22 < 4 (True) For x = -1: 81/22 < 4 (True) For x = 0: 81/22 < 4 (True) For x = 1: 81/22 < 4 (True) For x = 2: 81/22 < 4 (True) For x = 3: 81/22 < 4 (True) For x = 4: 81/22 < 4 (True) For x = 5: 81/22 < 4 (True) For x = 6: 81/22 < 4 (True)

From the above evaluations, we can see that the inequality is true for all integer values of x within the interval [-6, 6]. Therefore, the inequality has an infinite number of integer solutions within the given interval.

I hope this helps! Let me know if you have any further questions.