Question

Решите неравенство 4х^2>9х

Answer 1

Короче смотри все на фото)

Answer 2

Решение на рисунке.

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Answer 3

To solve the inequality 4x^2 > 9x, we need to find the values of x that satisfy the inequality. Here's the step-by-step solution:

1. Move all terms to one side of the inequality to have a quadratic expression greater than zero: 4x^2 - 9x > 0

2. Factor the quadratic expression: x(4x - 9) > 0

3. Determine the critical points by setting each factor to zero and solving for x: x = 0 (from x = 0) 4x - 9 = 0 (from 4x - 9 = 0) 4x = 9 x = 9/4

4. Create a number line and mark the critical points: -∞ |-----0-----9/4-----|

5. Test the inequality in each interval defined by the critical points. Choose a test point within each interval and check if the inequality holds true:

• Test x = -1 (any value less than 0): 4(-1)^2 - 9(-1) > 0 4 + 9 > 0 13 > 0 The inequality is true in this interval.

• Test x = 1 (any value between 0 and 9/4): 4(1)^2 - 9(1) > 0 4 - 9 < 0 -5 < 0 The inequality is false in this interval.

• Test x = 3 (any value greater than 9/4): 4(3)^2 - 9(3) > 0 36 - 27 > 0 9 > 0 The inequality is true in this interval.

6. Determine the solution based on the truth values in the intervals:

The inequality is satisfied in the intervals (-∞, 0) and (9/4, ∞). Therefore, the solution to the inequality is: x < 0 or x > 9/4